How many rational numbers exist between zero and one?
Infinity...................
A mathematician walked into a bar and he told the bartender “I want a shot of whiskey for myself.”
Bartender says “Coming right up... anything else?”
The mathematician responded “Yes. I’ve got 50 friends with me. The first one wants half a shot. The second wants half of that - a quarter shot. The third wants half of _that_... and every succeeding friend wants half the amount of the previous one.”
The bartender immediately puts two shot glasses on the bar and fills both, saying “Here ya go — your last friend can finish off whatever’s left over.”
The mathematician paid for the drinks and thanked the bartender, who responded by saying “I can appreciate a man who knows his limits.”
A countable infinity. The same number as the number of all rational numbers!