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.
We know that
Multiplying both sides by , we have
If the proof above does not convince you, there is another proof below.
Multiplying both sides by , we have .
Subtracting, we have
Photo Credit: Marco Arment via Flickr Creative Commons