Category Archives: arithmetic

Arguments for 0.9999… Being Equal to 1

Recently I tried to explain to my 11-year-old son why 0.9999… equals 1.  The standard arguments for (at least the ones I’ve seen) assume more math background than he has.  So I tried another couple of arguments, and they seemed … Continue reading

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Proof of the Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic states the following: Every integer greater than 1 can be represented uniquely as the product of prime numbers. Another way to put this is that every integer has a unique factorization.  For example, 60 factors … Continue reading

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A Mathematical Riddle

This past weekend I attended the wedding of a former student, Jake Linenthal.  On the dinner tables at the reception were sheets of paper containing a Mad Libs-style story of how Jake and his wife Abby got engaged, as well … Continue reading

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How Fast Do Factorials Grow?

Sometimes it’s hard to grasp just exactly how fast certain rapidly increasing functions – like exponentials and factorials – actually grow.  This was brought home to me a few years ago when I wrote some code for solving a problem … Continue reading

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Checking Multiplication via Digit Sums

Last week a friend who is a fourth grade teacher came to me with a math problem.  The father of one of his students had showed him a trick for checking the result of a three-digit multiplication problem.  The father … Continue reading

Posted in arithmetic, elementary number theory | 4 Comments