/sci/ - Science & Math

>>11572851
>is defined to be

By whom. You?

You need to face it. The set of Real numbers is DEFINED by the exclusion of infinitesimals. So using them to prove .999... = 1, is the same as using Whole numbers to prove that 1/2 = 0.

There is nothing real about Real numbers. If you are counting electrons, one half DOES equal zero. But that doesn't prove that 1/2 never exists, and neither can you use the limits of the Real set to say that infinitesimals don't exist.

>... and the limit of the series 4, 4, 4, 4, 4, 4, ... is Pi.
> No.
Why not? Try and explain the mistake, instead of just endlessly appealing to your misunderstanding of authority.

Every proof of 1=.999... ultimately has the same flaw:

The set of Real numbers was specifically designed to exclude non-zero infinitesimals. As a result, any proof involving the Real set assumes the conclusion you are trying to prove. Infinitesimals don't exist in the Reals for the same reason that fractions don't exist in the Integers.

This is the OPPOSITE of a proof.

As the video I linked to above shows, infinitesimals have been important since Issac Newton's time. There was an emotional need to deny them for a while, but for serious maths, that is over now.

Anyone questioning 1=.999... is thinking about infinitesimals. Responding with "proofs" based on real numbers is obnoxious and undermines people's faith in math and science. It needs to stop.