Tag Archives: counting numbers

October 12, 2015

Inevitable Math

$Math!$

Oh, no! Not math again!

Among those who try to imagine alien first contact, many believe that mathematics will be the basis of initial communication. This is based on the perceived universality and inevitability of mathematics. They see math as so fundamental any intelligence must not only discover it but must discover the same things we’ve discovered.

There is even a belief that math is more real than the physical universe, that it may be the actual basis of reality. The other end of that spectrum is a belief that mathematics is an invented game of symbol manipulation with no deep meaning.

So today: the idea that math is universal and inevitable.

44 Comments | tags: alien math, cardinal numbers, cardinality, counting, counting numbers, first contact, Leopold Kronecker, math origins, math theory, mathematics, natural numbers, numbers, Philosophy of Math, rational numbers, real numbers, Theory of Mathematics | posted in Math, Opinion

June 25, 2014

Sideband #55: Numbers & Sets

By Wyrd Smythe

In this post I’ll show how Set Theory allows us to define the natural numbers using sets. It’s admittedly a very abstract topic, but it’s about something very common in our experience: counting things. Seeing how numbers are defined also demonstrates (contrary to some false notions) that there is a huge difference between a number and how that number is “spelled” or represented.

Note: I am not a mathematician! This topic is right on the edge of my mathematical frontier. I wanted this addendum to the previous post but be aware I may misstep. I welcome any feedback from Real Mathematicians!

But go on anyway… keep reading… I dare ya!

8 Comments | tags: counting, counting numbers, natural numbers, numbers, set theory, successor function | posted in Math, Sideband

October 20, 2012

Infinity is Funny

By Wyrd Smythe

You probably have some idea of what infinity means. Something that is infinite goes on forever. But it might surprise you to know that there are different kinds of infinity, and some are bigger than others!

As an example, a circle has an infinite number of points. (Yet the circumference of the circle has finite length.) Compare that to a straight line with infinite length. Both have infinitely many points but does the finite length circle have fewer? [The answer is no.]

To understand all this, we have to first talk a bit about numbers.

32 Comments | tags: countable, counting numbers, Georg Cantor, infinity, irrational numbers, natural numbers, pi, rational numbers, uncountable | posted in Math, Science