This is the first 1,000 characters of 1060 words (4.24 pages) in the essay titled Infinity
Most everyone is familiar with the infinity symbol, the one that looks like the number eight tipped over on its side. Infinity sometimes crops up in everyday speech as a superlative form of the word many. But how many is infinitely many? How big is infinity? Does infinity really exist?
You can't count to infinity. Yet we are comfortable with the idea that there are infinitely many numbers to count with; no matter how big a number you might come up with, someone else can come up with a bigger one; that number plus one, plus two, times two, and many others. There simply is no biggest number. You can prove this with a simple proof by contradiction.
Proof: Assume there is a largest number, n. Consider n+1. n+1*n.
Therefore the statement is false and its contradiction, “there is no largest integer,” is true. This theorem is valid based on the “Validity of Proof by Contradiction.”
In 1895, a German mathematician by the name of Georg Cantor introduced a way...
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