Transcendental Numbers (extra footage) - Numberphile
Main video is at: http://youtu.be/seUU2bZtfgM This is some extra stuff from Simon Pampena we didn't use in the first video! More links & stuff in full description below ↓↓↓ NUMBERPHILE...
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Well, it's important because it's knowledge, the knowledge of numbers. The algebraic numbers are the ones that we're the most familiar with. But in a sense, there's hardly any of them compared to transcendental numbers. Algebraic numbers are actually countable, or listable is another way of saying it. So it's actually quite a small infinity. It's the smallest infinity. But on the real number line, you've got a bigger infinite. It just so happens that most of the numbers on the real number line are transcendental. And we didn't know that until we discovered transcendental numbers. So this is really recent information in terms of the long history of maths that humanity's been covering over 2,000 years. This is a ...
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Well, it's important because it's knowledge, the knowledge of numbers. The algebraic numbers are the ones that we're the most familiar with. But in a sense, there's hardly any of them compared to transcendental numbers. Algebraic numbers are actually countable, or listable is another way of saying it. So it's actually quite a small infinity. It's the smallest infinity. But on the real number line, you've got a bigger infinite. It just so happens that most of the numbers on the real number line are transcendental. And we didn't know that until we discovered transcendental numbers. So this is really recent information in terms of the long history of maths that humanity's been covering over 2,000 years. This is a ...
