Daily Archives: March 10, 2020

Number Islands

In the Rational vs Real post I mentioned that real numbers were each “an infinitely tiny island separated from direct contact with all other numbers.” The metaphor of each real number as an island comes from how, given any real number, it’s not possible to name the next (or previous) real number.

It’s easy enough to name a particular real number. For instance 1.0 are 3.14159… real numbers. There are infinitely many more we can name, but given any one of them, there is no way to get to any other number other than by explicitly naming it, too.

This applies to a variety of numeric spaces.

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