## Maths Infinity

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

That’s all.

$\dpi{300} \bg_white \begin{matrix} s: \mathbb{N} \to \mathbb{N} \\ s \mapsto s+1 \end{matrix}$
($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. 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. $\dpi{300} \bg_white \underbrace{ {{{{{{{{{{{{3^3}^3}^3}^3}^3}^3}^3}^3}^3}^3}^3}^{\cdots} } }_{ 3^{3^{3^{3^{\cdots}}}} \text{ times} }$ 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.