State Your Basis

[Of Special Interest to Young Men and Women]

"Prove that two and two does not always equal four." This problem, which appeared on a college mathematics test, may puzzle many adults, for today in new mathematics courses students are learning, even in elementary schools, that the once invariable fact of 2+2=4 is not always true.

Instead, the number system, or basis, being used must be stated. Today's mathematics courses are not limited to one system of ten digits but are aimed at teaching students the unlimited and practical usage of other number systems, one of which is utilized by modern computers. So in a three-digit system, 2+2=11 and in a four-digit system, the answer is 10. These answers might seem unreasonable if we did not first define their basis, but when we do, we know that the answer can't be 4, because there is no digit 4 in either system.

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Demonstrating True Independence
July 3, 1965
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