**Introduction**

There are certain concepts in mathematics that are counterintuitive. In this post, we discuss one of these concepts — the elementary proof that . The symbol indicates that there are infinitely many ‘s to the right hand side of the decimal point. The proof of this theorem is extremely easy; however, to be able to appreciate it will require understanding of the concept of limits and infinity.

**Theorem: **

**Proof 1 **

We know that

.

Multiplying both sides by , we have

If the proof above does not convince you, there is another proof below.

**Proof 2**

Let .

Multiplying both sides by , we have .

Subtracting, we have

.

.

Therefore, .

***

Photo Credit: Marco Arment via Flickr Creative Commons

First of all, 0.999…=1 is not a theorem. Secondly, it’s false.

https://www.filesanywhere.com/fs/v.aspx?v=8b6966895b6673aa6b6c

And a discussion where you will learn more mathematics than you learned in all your years.

Read especially the comments made by John Gabriel.

http://www.spacetimeandtheuniverse.com/math/4507-0-999-equal-one-369.html