Basefinifinity

Basefinifinity (∞↘) is a relatively small number. written out, it is:

$\overbrace{ \infty_{\infty_{\cdots_\infty}} }^{\infty}$ , where the subscript represents base conversion.

First, an even smaller number: Basefinity. Basefinity is infinity converted to base infinity.

This number can be approximated to (∞+1)[∞]2. since 10_∞ = ∞+1, 100_∞ ≈ ∞² = ∞×∞, 1000_∞≈²∞=∞^∞.

Next, we need to convert to base-basefinity. which should be roughly (∞_∞+1)[∞_∞]2. This expands to: ((∞+1)[∞]2)[(∞+1)[∞]2]2. this can be (very roughly) approximated to ∞{{1}}3. This way basefinifinity can be approximated to {∞,∞,1,2}.

This can be extend further, and at it's (small) maximum, it reaches roughly 4&∞ (ampersand denotes "array of" operator)