03-10-2009, 01:37 PM
Allyson Wrote:.999... is real but it is irrational, meaning it could never be expressed as a fraction. 1 = 1/1.
By definiton 1 = the limit the sequence {1/1 + 1/1 + 1/1 + ...}
but it is also true that 1= the limit of the sequence {9/10 +99/100 +999/1000 + ...}
which again is using the definiton of the real numbers, thus both equal one by definiton.
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