03-11-2009, 09:51 AM
motorboatking Wrote:1=1
.999..... doesn 't have a specific value. Yet it's infinitely less than 1.
Yes it does, just like 1/2 = 2/4 = 4/8, etc 0.999... = 1, they are the same number based on the DEFINITON of the real numbers, I don't get how that is hard to understand, there is only one definition for real numbers...
As found on a math site:
In the last few decades, researchers of mathematics education have studied the reception of this equality among students, many of whom initially question or reject this equality. Many are persuaded by textbooks, teachers and arithmetic reasoning as below to accept that the two are equal. However, they are often uneasy enough that they offer further justification. The students' reasoning for denying or affirming the equality is typically based on one of a few common erroneous intuitions about the real numbers; for example that each real number has a unique decimal expansion, that nonzero infinitesimal real numbers should exist, or that the expansion of 0.999
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