Algebra

Proof that 0.9 repeating is equal to 1

x = 0.9...

10x = 9.9...

10x - x = 9.9... - 0.9...

9x = 9

x = 1

Description

This is something my friend taught me at one point; it is a mindblowing concept and I think it is really relevent to understanding math at a deeper level.

It can also be understood in other ways, such as:

1/3 = 0.3...

2/3 = 0.6...

3/3 = 0.9...

Also simply understanding the idea of infinity, and that if two real numbers are different, there must be some number inbetween. There is no number inbetween 0.9... and 1