Mathemathics in expanding brain memes

Tiny_brain.jpg: Infinity is a number
Normal_brain.jpg: 0.999...=1
Illuminated_brain.jpg: 1+2+3+4+5+...=-1/12
Enlightened_Mind.jpg: Real numbers aren't real
Master_of_All_Cosmos.jpg: Ultrafinitism

>>4
Finitism means you can't use shortcuts, like the axiom of excluded middle, being forced to prove everything the hard way. In general, finitist mathematics is order of magnitude harder and proofs require more steps. For example, take a look at Wildberger's lectures, where he proves high school stuff without using irrational numbers, carefully avoiding introducing expressions such as sqrt(2).