Conceiving of ∞ as a mathematician is simple. You start counting, and don’t stop.

That’s all.

successor function
($i++ for programmers)

Which is why seems very small to the mind of a mathematician.

With projective geometry you can map to a circle, in which case there is a point-sized hole at the top where you can put ∞ (or −∞, or both).

Same thing with the Riemann Sphere.

stereographic projection of the Riemann sphere

So to them ∞ is very reachable. It’s just a tiny point.

Graham’s Number

It takes much more mental effort to conceive of Graham’s Number than ∞. It took me several hours just to begin to conceive Graham’s number the first time I tried.

\underbrace{     {{{{{{{{{{{{3^3}^3}^3}^3}^3}^3}^3}^3}^3}^3}^3}^{\cdots}  }       }_{   3^{3^{3^{3^{\cdots}}}}  \text{ times}  }

Graham’s Number is basically a continuation of the above, recursed many times. Maybe I’ll do a write-up another time but really you can just look at Wikipedia or Mathworld. It’s absolutely mind-blowing.

Bigger

Here’s what’s weird. Infinity is obviously bigger than Graham’s Number. But Graham’s Number takes up more mental space. Weird, right?

EDIT: Maybe ∞ takes up less mental space than g64 because its minimal algorithmic description is shorter.

25 notes

  1. clazzjassicalrockhop reblogged this from isomorphismes
  2. noisesoundsignal reblogged this from isomorphismes and added:
    Math Infinity Conceiving of ∞ as a mathematician is simple. You start counting, and don’t stop. That’s all. ($i++ for...
  3. squint-scowl answered: Though some infinities might be larger than others. Consider cardinalities!
  4. davidaedwards answered: The Normal Distribution is conceptually much more complex than the Binomial Distribution; but computationally much simpler.
  5. thedoctor1994 answered: woah
  6. isomorphismes posted this