Sweet Reason: A Field Guide to Modern Logic by James M. Henle & Jay L. Garfield & Thomas Tymoczko

Author:James M. Henle & Jay L. Garfield & Thomas Tymoczko [Henle, James M.]
Language: eng
Format: epub
Publisher: Wiley
Published: 2012-04-11T22:00:00+00:00

Thus we reach the number 1. Now try another number, say 23.

Again we reach 1. Will this always happen?

This is known as the Collatz “3n + 1” problem. The evidence that it will always happen is strong. Using computers, mathematicians have checked that every number below 1 000 000 000 000 reaches 1. Is that enough?

As we said, strange things can happen in mathematics. There is a statement of mathematics that is also true for all numbers below 1 000 000 000 000 (the exact statement is not important or attractive). Unfortunately, it’s been proven that this statement is not true for all numbers. All that’s known, however, is that it’s false for some number below

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