Infinity Paradoxes - Numberphile09:45

Infinity Paradoxes - Numberphile



A lot of people don't realize that infinity is actually a concept, NOT really a number. Infinity describes something that is "unlimited" or "unbounded," and is, therefore, more of an imaginative concept, rather than something practical. In the photo to the right, for example, the horizon line might look infinitely far, but obviously the ocean ends at some point.

By the way, the title Beyond Infinity does not refer to a number or anything past infinity, but rather ideas beyond the concept of infinity. For example, beyond the idea of infinity are types of infinity (see below). 

Types of InfinityEdit

Infinity. The concept of infinity is often thought of as infinity in a positive direction, that is: 1, 2, 3, 4, 5, 6, 7... 

Negative Infinity. Infinity in a negative direction, that is: -1, -2, -3, -4, -5, -6, -7...

Countable Infinity. The mathematician Georg Cantor developed many of the ideas and applications for infinity, including many concepts around infinite sets. Countable infinity is the idea that, given an infinite amount of time, the set of integers could be infinitely counted. In other words, a theoretical person could count: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14... and so on without stopping.

Uncountable Infinity. The same theoretical process for countable infinity could not, however, count the set of real numbers. For example, starting from zero, try counting all of the fractional numbers. Where would you start? .1 or .01 or .001 or .0001 or .00001 or maybe .000001? Because there could always be a smaller decimal, this attempt is uncountable.

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