To Infinity… And Beyond?
Feb25

To Infinity… And Beyond?

“If you could count for a year, Would you get to Infinity, Or somewhere in that vicinity?” —  That’s Mathematics, Tom Lehrer. So, what is Infinity? In classical times, infinity was a word that simply denoted the possibility of always generating new objects,that is, never running out of objects of a certain type. For example, when Euclid asserts that there are infinitely many prime numbers, he states it thus...

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What the Tortoise said to Achilles, by Lewis Carroll
Feb11

What the Tortoise said to Achilles, by Lewis Carroll

What follows is a short story written by Lewis Carroll, and published in 1895. It explores some anomalies of Logic, suggesting that it’s incomplete, or empirical. This famous piece drew responses from celebrated logicians such as Bertrand Russel, and Peter Winch. Achilles had overtaken the Tortoise, and had seated himself comfortably on its back. “So you’ve got to the end of our race-course?” said the Tortoise....

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