July 2013
Intermediate to advanced
282 pages
6h 28m
English
Content preview from Good MathBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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What Does It Mean, and Why Does It Matter?
Irrational and transcendental numbers are everywhere. Most numbers aren’t rational. Most numbers aren’t even algebraic. That’s a very strange notion: we can’t write most numbers down.
Even stranger, even though we know, per Cantor, that most numbers are transcendental, it’s incredibly difficult to prove that any particular number is transcendental. Most of them are, but we can’t even figure out which ones!
What does that mean? That our math-fu isn’t nearly as strong as we like to believe. Most numbers are beyond us. Here are some interesting numbers that we know are either irrational or transcendental:
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e: transcendental
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π: transcendental
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The square root of 2: irrational, but algebraic
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The ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.