/sci/ - Science & Math

I know nothing about mathematics, but I did hear that 0.999... = 1. I was thinking about it for a moment, and I thought of something that I think may be a proof of it. I didn't find it among other common proofs of it, so is it just trivial, or a load of shit? Here it goes.

0.9999.. is infinitely close to 1, because there is no specific number that is a distance between them.

Therefore (1-0.999...) is infinitely close to zero.

Therefore 1/(1 - 0.99..) is infinitely close to infinity.

Now a real number cannot be infinitely close to infinity, as any real number can have one higher than it. Therefore it is infinite.

Therefore (1 - 0.99..)=0

Conclusion: 0.99... = 1

>>15242713
sauce