Oops, I Broke Math

One of the great bickering contests of the Internet regards the equality, or lack thereof, of the number 0.999… with the number 1. This is one of the not-so-great proofs provided by the “not equal” camp:

0.999 ≠ 1
0.9999999 ≠ 1
0.999999999999999999 ≠ 1
0.999999999999999999999999999999999999999999 ≠ 1
Therefore, 0.999… ≠ 1.

Despite it not being all that great of a proof, this is apparently enough to convince many people of the inequality of these two numbers. I can prove something else of interest using the same logic:

3.141 ≠ pi
3.1415926 ≠ pi
3.141592653589793238 ≠ pi
3.141592653589793238462643383279502884197169 ≠ pi
Therefore, pi ≠ pi.

But wait…. If pi doesn’t equal itself, then that means… the reflexive axiom is disproven! Countless geometry proofs fall apart! Nobody is certain that 42 is equal to 42! People can’t get out of work because their employers can’t tell that 5 PM is equal to 5 PM!

Or we could accept that a truncated non-ending number never counts as the non-ending number itself. …Nah, let’s do things my way; I like chaos. >:-D

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2 thoughts on “Oops, I Broke Math

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