Infinity Paradoxes

Connections List
 * Infinity
 * Paradoxes

From https://www.youtube.com/watch?v=dDl7g_2x74Q numberphile

Hilbert Hotel - inf rooms all full, add people by shifting them down

Gabriels trumpet - something like 1/x revolved on x axis, infinite area but finite volume. To paint the surface you need inf paint? but to fill with the same paint? the difference between an area and a volume and the volume that paint occupies

Dartboard - probability that dart will hit exact mathematical point. 0 and dart will never hit any point or >0 and sum of probabilities of infinite points is inf /what if probability is a special type of 0?/

Double your money - how much would you pay to enter game which begins at $1 and on coinflip doubles pot or cashes out, game done? expected value is inf sum of 1/2. /maybe if I could play the game an inf number of times?/