Eff this, philly mike is an idi0t, ask zdunklee.

[zdunklee]

NO I DIDN'T, I NEVER EVER MULTIPLIED TO GET THAT... how hard is that to understand, you are looking at them as seperate statements which they are not, they are equivalent statements from one line to the next.

Also, 8.999... = 9 anyway.

what do you mean you never multiplied???

x = 0.9999...
10x = 9.9999... 10*0.999... =9.999...
10x - x = 9.9999... - 0.9999... 10*0.999...-0.999... = 9
9x = 9
x = 1.


those are multiplication so why is 9x any different

and 8.999... only equals 9 if you go along with the assumption that 0.999 = 1 which is what you were supposed to be showing proof of when you posted the statement itself.


The whole bases of what you are talking about with real numbers is working with the assumption that 0.999... = 1

It is not an assumption, that is what I am trying to get across, it is the very definiton of the Real numbers. A real number is defined as a sequence of Rational numbers whose limit = x, where x can be any real number you want and I can find a sequence of Rational numbers that it is equal to. Thus every real number is the limit of a sequence of Rationals.

For example SQRT(2) = , where an=3/2.

Also SQRT(2) is the reason that the real numbers were created in the first place, before the 1500's there was no such thing as the real numbers and SQRT(2) was considered an imaginary number.

[Philly Mike]

but there is nothing to definitely show that 0.999... = 1

you can have no problem showing me that 1 = 1
you have 1 apple it is 1 apple.
you have .50 of an apple you have .50 or half of an apple. you have 0.999... of an apple you probably have an apple that is about an ultra-microscopic piece of the skin.okay i keep screwing my mind up.
you have an apple missing an ultra microscopic piece of skin.

[zdunklee]

Yes, but in mathematics you must work inside the definitons of the system you are using. Which is what causes the result in the first place. Opinions don't mean anything no matter who you are, if you can't prove what your thinking is based on the definitions and any other previously proved work then your thinking is wrong.


Here is the best I can do for you: Real numbers are defined as limits of sequences of Rational numbers.

Limit {0, 9/10, 99/100, 999/1000,...} = 1 and that sequence is 0.999...

[dingdongyo]

I blame RockMonster for this thread...

eff you dude

i blame mike.

is verizon hiring?

[zdunklee]

You think I could get a job at Verizon? I might be overqualified on the math end of things as I think anything beyond HS is overqualified to work at verizon.

[Philly Mike]

I blame RockMonster for this thread...

eff you dude

i blame mike.

is verizon hiring?

I blame both

eff you rock , and mike. effing jerks

Limit {0, 9/10, 99/100, 999/1000,...} = 1 and that sequence is 0.999...

I understand that this was shown in your calculus thing. but this is just a longer fancier way of saying 0.999... = 1 without showing how it equals 1
as i said with the apple 0.999... of an apple is the apple with basically a molecule missing from the skin. but that is still not a whole apple. it basically rounds to being a whole apple but literally it is not whole. just like 0.999... is not a whole it is missing that very little bit to make it 1

[dingdongyo]

i blame mike.

is verizon hiring?

I blame both

eff you rock , and mike. effing jerks

it's cool, mike. i just hope one day, you realize how knave you're being.

[taekahn]

Mike, by breaking it down to slices of apples, you're again reducing an infinite number into an extremely long, yet finite number, even if subconsciously so. The issue doesn't with .999.. being equal to zero, but rather with your conception of the infinite.
Free your mind.

[zdunklee]

i blame mike.

is verizon hiring?

I blame both

eff you rock , and mike. effing jerks

Limit {0, 9/10, 99/100, 999/1000,...} = 1 and that sequence is 0.999...

I understand that this was shown in your calculus thing. but this is just a longer fancier way of saying 0.999... = 1 without showing how it equals 1
as i said with the apple 0.999... of an apple is the apple with basically a molecule missing from the skin. but that is still not a whole apple. it basically rounds to being a whole apple but literally it is not whole. just like 0.999... is not a whole it is missing that very little bit to make it 1

No it is not, it is how the real numbers are defined, and it is the only way they are defined. Jesus, how many times do I have to say that.

Basically what you are arguing is like me saying this sentence is red. Now prove to me that it isn't.

[Philly Mike]

I blame both

eff you rock , and mike. effing jerks


I understand that this was shown in your calculus thing. but this is just a longer fancier way of saying 0.999... = 1 without showing how it equals 1
as i said with the apple 0.999... of an apple is the apple with basically a molecule missing from the skin. but that is still not a whole apple. it basically rounds to being a whole apple but literally it is not whole. just like 0.999... is not a whole it is missing that very little bit to make it 1

No it is not, it is how the real numbers are defined, and it is the only way they are defined. Jesus, how many times do I have to say that.

Basically what you are arguing is like me saying this sentence is red. Now prove to me that it isn't.

stating a sentence is a color is different than stating something in math. there is always a way to prove something equals something else. You can prove 1/2 equals .50 by dividing, you can prove 1 1/4 = 1.25 the same way. but if you go ahead and try to prove .999... equals 1 there is no formula i have seen you show. language is something completely created by man. some of it describes real things but things like colors were named so. 1 represents a single object anything that is represented by a decimal is represented by something that is not a whole 1 so how could that make .999... anything but less than 1

Mike, by breaking it down to slices of apples, you're again reducing an infinite number into an extremely long, yet finite number, even if subconsciously so. The issue doesn't with .999.. being equal to zero, but rather with your conception of the infinite.
Free your mind.

so you're telling me that cutting an apple into 3 equal parts would be limiting it to being a finite number??

the whole thing is that .999... is like that frog trying to make it to that line always hopping half way. instead of the number getting lower than 1, it is always trying to make it up to 1 but it just keeps on in the infinite matter of .999...

[zdunklee]

No it is not, it is how the real numbers are defined, and it is the only way they are defined. Jesus, how many times do I have to say that.

Basically what you are arguing is like me saying this sentence is red. Now prove to me that it isn't.

stating a sentence is a color is different than stating something in math. there is always a way to prove something equals something else. You can prove 1/2 equals .50 by dividing, you can prove 1 1/4 = 1.25 the same way. but if you go ahead and try to prove .999... equals 1 there is no formula i have seen you show. language is something completely created by man. some of it describes real things but things like colors were named so. 1 represents a single object anything that is represented by a decimal is represented by something that is not a whole 1 so how could that make .999... anything but less than 1

And this is exactly what I expected you to say, math like language is completely created by man, that is my point, red is defined as a certain color, but it could have just as easily been defined differently and my sentence could in fact be red, as long as I choose to ignore the definitons that are accepted.

Much like you are choosing to ignore the definiton of the real number system.

[Philly Mike]

stating a sentence is a color is different than stating something in math. there is always a way to prove something equals something else. You can prove 1/2 equals .50 by dividing, you can prove 1 1/4 = 1.25 the same way. but if you go ahead and try to prove .999... equals 1 there is no formula i have seen you show. language is something completely created by man. some of it describes real things but things like colors were named so. 1 represents a single object anything that is represented by a decimal is represented by something that is not a whole 1 so how could that make .999... anything but less than 1

And this is exactly what I expected you to say, math like language is completely created by man, that is my point, red is defined as a certain color, but it could have just as easily been defined differently and my sentence could in fact be red, as long as I choose to ignore the definitons that are accepted.

math is not a language, red can be shown by examples of red. there are no equations to show what language shows. however math is something more of the nature of science, everything that is thought of has to have proof in order to properly exist. all i want to see is the proof that this can actually apply physically, and so far i have seen nothing showing it except for a bunch of numbers giving different ways of saying .999... = 1 instead of an actual formula showing different from that. because if you do any process it doesn't work out as 1 but as it's own number like 5 + .999... = 5.999... or 9*.999... = 8.999... now you can just say that the first one =6 and the second =9 but you have nothing showing me how you get to that point without just truncating and rounding up.

[zdunklee]

This is where you are wrong, Math is a language that we use to explain things that occur in the real world. Math is called the Universal Language because no matter what language you speak you can understand basic math.

I have shown you why it is equal based on the very foundation of the real numbers, you are choosing to ignore how they are defined. Look up the effing definiton of real numbers and then show me I am wrong based on that definiton.

From the history of mathematics:

The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals[10], was probably that of numbers: the realization that two apples and two oranges (for example) have something in common.

In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time

[Philly Mike]

[quote="zdunklee"]This is where you are wrong, Math is a language that we use to explain things that occur in the real world. Math is called the Universal Language because no matter what language you speak you can understand basic math.

I have shown you why it is equal based on the very foundation of the real numbers, you are choosing to ignore how they are defined. Look up the effing definiton of real numbers and then show me I am wrong based on that definiton.

From the history of mathematics:

The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals[10], was probably that of numbers: the realization that two apples and two oranges (for example) have something in common.

In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time

[zdunklee]

Or:

Most of the mathematical notation in use today was not invented until the 16th century.[17] Before that, mathematics was written out in words, a painstaking process that limited mathematical discovery. In the 18th century, Euler was responsible for many of the notations in use today. Modern notation makes mathematics much easier for the professional, but beginners often find it daunting. It is extremely compressed: a few symbols contain a great deal of information. Like musical notation, modern mathematical notation has a strict syntax and encodes information that would be difficult to write in any other way.


It is a science, but it is also a language, that has changed a lot over time and is very well documented, the current symbols we use for number might not be the symbols that are used in a few hundred years. Just like our symbols were not around until the 1600's.

[Philly Mike]

yes there is a language for mathematics because it has it's own terminology just like in science. do you think the periodic table of the elements wouldn't count as it's own language? because every one of those elements were given a name. but those elements needed proof of existence before being named, anything without proof is just a theory. so .999... would have to have actual proof of = 1 other than just someone saying it equals 1. Shit i could say 1 = 2 but that doesn't make it true, because it isn't and that can be proven by the very bases of what numbers are.

[speedbump]

Philly Mike you know very little about what you're arguing, but you think you know a lot.

I found the problem! Now how do we solve it? Logic isn't going to work, because zdunklee has already defeated you on that front and you still keep treading water. You're making yourself look like an idiot, and if you want to salvage some respect admitting defeat is probably your best bet.

[zdunklee]

It does, that is the effing proof I have shown you, that is based on the definitons of the real effing numbers. Just continue to ignore the effing definitons, cause all science is based upon them and if they are ignored then all science is wrong.

[Philly Mike]

Philly Mike you know very little about what you're arguing, but you think you know a lot.

I found the problem! Now how do we solve it? Logic isn't going to work, because zdunklee has already defeated you on that front and you still keep treading water. You're making yourself look like an ambulance driver, and if you want to salvage some respect admitting defeat is probably your best bet.

all i have been asking for is proof. that is it. i have not been trying to argue just for it. but i have seen no proof. I never said I knew more than him. I have just been stating it as i see it.

It does, that is the effing proof I have shown you, that is based on the definitons of the real effing numbers. Just continue to ignore the effing definitons, cause all science is based upon them and if they are ignored then all science is wrong.

science is based off of proof, evidence showing why something is what it is. how it got like that. all you are giving me is a definition, not how it was reached or what reason it is that way. A definition in science is useless without the proof of why it is that way.

[zdunklee]

Yes, and I have presented that in logical arguments while you continue to make non-sensical arguments.

The proofs in science are based of definitons of mathematics if they use any mathematics at all, and if you choose to ignore the definiton of real numbers, then all science that has used real numbers in their proofs are now wrong because they relied on a definiton that does not exist.


Also, I don't know if you noticed, but you are the only one continuing to argue this, why is that? Could it be because no one else here has a proof that 0.999... =! 1? I have shown you several proofs that say it does equal 1, I challange you to come back with a real argument and proof that it does not equal 1, as that is the ONLY way your opinion matters. Opinion means nothing no matter how steadfast you hold to that opnion, without proof it just means your opinion is wrong.

[taekahn]

I have a question.
Mike, do you disagree with 1 + 0.111... = 1.111...?

[zdunklee]

I am done debating this topic, because a debate implies that all parties have intelligence in the subject matter, and clearly Mike, you only have enough to just get by for what you need it for. I don't want you to take that as an insult to your intelligence as I am sure there are many topics in which you are smarter than I, but math is not one of them.

Q.E.D.

[Philly Mike]

I am done debating this topic, because a debate implies that all parties have intelligence in the subject matter, and clearly Mike, you only have enough to just get by for what you need it for. I don't want you to take that as an insult to your intelligence as I am sure there are many topics in which you are smarter than I, but math is not one of them.

Q.E.D.

whatever, you may not have intended to insult my intelligence and i could care less how stupid you would think i am. I am trying to get to a real application of this, i have seen no use for this. if you look at the number itself it would be close to 1 but never reaching. i have seen the definition, I know what a Effing real number is, i know what a rational number is, i know what the Eff all of that stupid shit is. science uses the numbers needed for proof. I am not arguing the existance of real numbers or any of that shit. This just really makes no sense for actually using it for something other than it seeming there is a very slight difference where there supposedly isn't because that's how it is defined.

[zdunklee]

I'm just trying to be nice, I respect you here, and I don't want you to look like any more of an ambulance driver than you already are looking. I have seen posts here stating it, and I have recieved PM's saying much the same.

I was never arguing that there is any usefulness of 0.999... = 1, I am just saying that is how it is defined, therefore that is what it is. I could use your argument in Euclidean Geometry to say a line does not exist because no one can prove it exists. Drawing on a piece of paper isn't a proof (as a matter of fact there is no way to draw a perfectly straight line anyway, you can get really damn close but it still wouldn't be perfect), and there is no way to prove a line exists without using a line in the proof.

[Philly Mike]

I'm just trying to be nice, I respect you here, and I don't want you to look like any more of an ambulance driver than you already are looking. I have seen posts here stating it, and I have recieved PM's saying much the same.

I was never arguing that there is any usefulness of 0.999... = 1, I am just saying that is how it is defined, therefore that is what it is. I could use your argument in Euclidean Geometry to say a line does not exist because no one can prove it exists. Drawing on a piece of paper isn't a proof (as a matter of fact there is no way to draw a perfectly straight line anyway, you can get really damn close but it still wouldn't be perfect), and there is no way to prove a line exists without using a line in the proof.

what so now there are Effing a-holes that cant even say it to my face, speedbump may be a dick but he at least had the guts to say it out here. if that is the case Eff all of you. I was just trying to get an application out of it, okay i may have posted some points that may have put out the wrong impression of the point i was trying to make, but if any shit head has a problem with it and they Effing want to pm you about it instead of say something to me or ask me why or what the Eff ever else then they are just a pussy. Effing bullshit i was not going for any ridicule or any shit like that. I would have ended it and just said okay watever, no proof then nothing to it. but Eff anyone who decides not to say shit. Effing a-holes now i see where Effing people stand. it isn't like you actually have to look me in the face you are behind a keyboard if you Effing have a problem and dont have the balls to say it to me then i dont want to even deal with it.

Effing bullshit i dont need to deal with any a-holes like that. i get enough of that when i am not online.

[zdunklee]

I'm just trying to be nice, I respect you here, and I don't want you to look like any more of an ambulance driver than you already are looking. I have seen posts here stating it, and I have recieved PM's saying much the same.

I was never arguing that there is any usefulness of 0.999... = 1, I am just saying that is how it is defined, therefore that is what it is. I could use your argument in Euclidean Geometry to say a line does not exist because no one can prove it exists. Drawing on a piece of paper isn't a proof (as a matter of fact there is no way to draw a perfectly straight line anyway, you can get really damn close but it still wouldn't be perfect), and there is no way to prove a line exists without using a line in the proof.

what so now there are effing a-holes that cant even say it to my face, speedbump may be a dick but he at least had the guts to say it out here. if that is the case eff all of you. I was just trying to get an application out of it, okay i may have posted some points that may have put out the wrong impression of the point i was trying to make, but if any shit head has a problem with it and they effing want to pm you about it instead of say something to me or ask me why or what the eff ever else then they are just a pussy. effing bullshit i was not going for any ridicule or any shit like that. I would have ended it and just said okay watever, no proof then nothing to it. but eff anyone who decides not to say shit. effing a-holes now i see where effing people stand. it isn't like you actually have to look me in the face you are behind a keyboard if you effing have a problem and dont have the balls to say it to me then i dont want to even deal with it.

effing bullshit i dont need to deal with any a-holes like that. i get enough of that when i am not online.

Chill out man, they were just saying that you were not making yourself look intelligent about this subject, which I also believe. I don't think anyone believes that you are really an idiot about all things.

[Philly Mike]

that't not what you said. you said

I don't want you to look like any more of an ambulance driver than you already are looking. I have seen posts here stating it, and I have recieved PM's saying much the same.

and regardless people could Effing say shit to me. if you think i am an idi0t then you can say it. if you don't think something sounded right say it to me in a PM don't go ranting on to someone else about it then have it aired in front of me like this.


basically what your post says is that i am a Effing idi0t and you aren't the only one who thinks so and you have the PMs to prove it.
Eff off if you have to call me an idi0t over something stupid. No need to shit talk me behind my back if you have a problem.

[zdunklee]

To be clear I only think you are an ambulance driver about this, not that it helps. I thought it was clear that I wasn't the only one before my post cause I can think of at least 4-5 others off the top of my head that posted in here arguing the same thing I was.

[Philly Mike]

and I have recieved PM's saying much the same.

yeah because that says you are the only one... right???

make up your mind are you the one calling me stupid or are others calling me stupid. you cant even keep that straight. I dont give a Eff anymore if someone has a problem with me than they should have said so to me.

[zdunklee]

See the post above where I say clearly that 4-5 others have posted in this thread about your bad arguments, do you always just read parts of posts? Cause maybe that is the problem we are having...

To be clear I only think you are an ambulance driver about this, not that it helps. I thought it was clear that I wasn't the only one before my post cause I can think of at least 4-5 others off the top of my head that posted in here arguing the same thing I was.

^I thought that said that I don't think you are an idiot about anything but this and others agreed with me well before I pointed it out that they agreed with me...

[dingdongyo]

and I have recieved PM's saying much the same.

yeah because that says you are the only one... right???

make up your mind are you the one calling me stupid or are others calling me stupid. you cant even keep that straight. I dont give a eff anymore if someone has a problem with me than they should have said so to me.

i pm'd zdunk saying we need to let it go because you aren't accepting this truth and proof that everyone else in the mathematical world has accepted. it's like talking to "a brick wall," i believe i said.

and i've tried to say the same publicly several times, with a more comical spin.

lighten up.

[zdunklee]

^It wasn't just him, but still none of them implied anything more than your arguments were not making any sense at all, even some who initially agreed with you.

[Philly Mike]

^It wasn't just him, but still none of them implied anything more than your arguments were not making any sense at all, even some who initially agreed with you.

exactly my point. no need to talk shit behind my back. Like i said my point may have been diluted within the argument no need to effing go ahead and call me a effing idiot.

i pm'd zdunk saying we need to let it go because you aren't accepting this truth and proof that everyone else in the mathematical world has accepted. it's like talking to "a brick wall," i believe i said.

and i've tried to say the same publicly several times, with a more comical spin.

lighten up.

Lighten up??? How the eff would you feel if i said to you that "you are an idiot and i have PMs that other people feel the same way"

I don't think anyone would have that fly over well, no matter what it was about. So how the eff do you expect me to lighten up?

And all of this especially after the fact that throughout all of this I had talked shit about no one. If I have something to say to someone they see it. So yeah I am offended, this is bullshit to hear about yourself when you were actually being civil to others.

[uhohspagettio]

Holy Ess! Are you one of those people that when asked for directions will say "Drive 1.4532 miles and make a 90 degree turn to the north, continue on for 275 yards or 825 feet and make 90 turn to the west....etc. etc."

No, I am just saying that every single number has multiple representations and even in math the preferred way to write them is whatever one is the simpliest, which is why if you do get a number like 0.999... you write it as a 1.

I understand where everyone is coming from and I can't believe this thread has gone on for 6 pages. My point is, when would a normal person run into a time when they have to use this in their daily life? My company rounds their sales up to the nearest dollar if it's $.50 and over and down for $.49 and under. Just not sure where Joe or Jane Six-Pack would ever run into a situation where they would need this. I will now watch from the sidelines to see how this all works out. Please resume your math dirty talk. :o

[Philly Mike]

No, I am just saying that every single number has multiple representations and even in math the preferred way to write them is whatever one is the simpliest, which is why if you do get a number like 0.999... you write it as a 1.

I understand where everyone is coming from and I can't believe this thread has gone on for 6 pages. My point is, when would a normal person run into a time when they have to use this in their daily life? My company rounds their sales up to the nearest dollar if it's $.50 and over and down for $.49 and under. Just not sure where Joe or Jane Six-Pack would ever run into a situation where they would need this. I will now watch from the sidelines to see how this all works out. Please resume your math dirty talk. :o

Apparently none of this means shit, I am obviously an idi0t and nothing i say matters or makes any sense. but hey don't worry. as stupid as I am, I am sure sooner or later I will forget how to Effing turn on my computer so you may not have to worry about any more of this shit anyway.

[uhohspagettio]

I'm just trying to be nice, I respect you here, and I don't want you to look like any more of an ambulance driver than you already are looking. I have seen posts here stating it, and I have recieved PM's saying much the same.

I was never arguing that there is any usefulness of 0.999... = 1, I am just saying that is how it is defined, therefore that is what it is. I could use your argument in Euclidean Geometry to say a line does not exist because no one can prove it exists. Drawing on a piece of paper isn't a proof (as a matter of fact there is no way to draw a perfectly straight line anyway, you can get really damn close but it still wouldn't be perfect), and there is no way to prove a line exists without using a line in the proof.

what so now there are effing a-holes that cant even say it to my face, speedbump may be a dick but he at least had the guts to say it out here. if that is the case eff all of you. I was just trying to get an application out of it, okay i may have posted some points that may have put out the wrong impression of the point i was trying to make, but if any shit head has a problem with it and they effing want to pm you about it instead of say something to me or ask me why or what the eff ever else then they are just a pussy. effing bullshit i was not going for any ridicule or any shit like that. I would have ended it and just said okay watever, no proof then nothing to it. but eff anyone who decides not to say shit. effing a-holes now i see where effing people stand. it isn't like you actually have to look me in the face you are behind a keyboard if you effing have a problem and dont have the balls to say it to me then i dont want to even deal with it.

effing bullshit i dont need to deal with any a-holes like that. i get enough of that when i am not online.

I was with you the whole time Mike.

[uhohspagettio]

I understand where everyone is coming from and I can't believe this thread has gone on for 6 pages. My point is, when would a normal person run into a time when they have to use this in their daily life? My company rounds their sales up to the nearest dollar if it's $.50 and over and down for $.49 and under. Just not sure where Joe or Jane Six-Pack would ever run into a situation where they would need this. I will now watch from the sidelines to see how this all works out. Please resume your math dirty talk. :o

Apparently none of this means shit, I am obviously an idi0t and nothing i say matters or makes any sense. but hey don't worry. as stupid as I am, I am sure sooner or later I will forget how to effing turn on my computer so you may not have to worry about any more of this shit anyway.

Mike, when I mentioned dirty talk, it was not a slam on you. I hadn't read to the end of the thread where you got pissed and used a few choice words, which if I were in your place, would have used as well. My comment was to ZDunk and his nerdy math talk that is only good for turning on young, naive freshman dork coeds.

[Philly Mike]

Apparently none of this means shit, I am obviously an idi0t and nothing i say matters or makes any sense. but hey don't worry. as stupid as I am, I am sure sooner or later I will forget how to effing turn on my computer so you may not have to worry about any more of this shit anyway.

Mike, when I mentioned dirty talk, it was not a slam on you. I hadn't read to the end of the thread where you got pissed and used a few choice words, which if I were in your place, would have used as well. My comment was to ZDunk and his nerdy math talk that is only good for turning on young, naive freshman dork coeds.

I know you didn't refer to me. sorry if it came off that way.

[zdunklee]

As far as a normal everyday person using it, they wouldn't. Only scientists and mathematicians would ever come across this issue.

But to argue that because you don't use it, therefore it isn't true doesn't make any sense either. I don't use hardly any of what I learned in college in my daily life, actually this thread is the first time I have ever used something I learned in any of my mathematics courses outside of college/tutoring. Most of the stuff you do as a mathematics major will never been seen by a "normal" person, just scientists and mathematicians.

It is the way it is because it was defined as such, much like my earlier example that the color red is what it is because it was defined as such. All of mathematics is defined based on the axioms of set theory (except Geometry which has it's own 5 axioms). An axiom is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths.

Thus everything in mathematics is technically "made up" but it is done so by a very specific set of rules.

[zdunklee]

In mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". In both senses, an axiom is any mathematical statement that serves as a starting point from which other statements are logically derived. Unlike theorems, axioms (unless redundant) cannot be derived by principles of deduction, nor are they demonstrable by mathematical proofs, simply because they are starting points; there is nothing else from which they logically follow (otherwise they would be classified as theorems).


Ha, what the hell, who changed the title of this thread? For the record I have said that mike is not an idi0t about anything but why mathematics is the way it is.