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edited May 7, 2020 at 18:28

Starting with some mind blowing paradoxes like asking the famous Russel's set paradox- does a set, that consists of all the sets that don't consist of themselves, consists of itself? (If it does - it doesn't, if it doesn't - it does).
Establishing the term of bijective functions, and with finite examples explainexplaining the motivation to define two equivalent sets as two that hashave a bijection between them.
A very cool and intuitive definition for an infinite set - a set which is equivalent to a strict subset of itself. It is nice to demonstrate with the Natural numbers and the Even numbers.
After the bijection term is well-established, it is time for Cantor's Diagonal Argument, to show that there could not be a bijection from the Natural numbers to the unit setsegment. I think this is probablymight just be the best 'party trick' to use when you want someone to get enthusiastic about set theory, thoughtthough I find it necessary to talk a bit about bijections first.

Starting with some mind blowing paradoxes like asking the famous Russel's set paradox- does a set, that consists of all the sets that don't consist of themselves, consists of itself? (If it does - it doesn't, if it doesn't - it does).
Establishing the term of bijective functions, and with finite examples explain the motivation to define two equivalent sets as two that has a bijection between them.
A very cool and intuitive definition for an infinite set - a set which is equivalent to a strict subset of itself. It is nice to demonstrate with the Natural numbers and the Even numbers.
After the bijection term is well-established, it is time for Cantor's Diagonal Argument, to show that there could not be a bijection from the Natural numbers to the unit set. I think this is probably the best 'party trick' to use when you want someone to get enthusiastic about set theory, thought I find it necessary to talk a bit about bijections first.

Starting with some mind blowing paradoxes like asking the famous Russel's set paradox- does a set, that consists of all the sets that don't consist of themselves, consists of itself? (If it does - it doesn't, if it doesn't - it does).
Establishing the term of bijective functions, and with finite examples explaining the motivation to define two equivalent sets as two that have a bijection between them.
A very cool and intuitive definition for an infinite set - a set which is equivalent to a strict subset of itself. It is nice to demonstrate with the Natural numbers and the Even numbers.
After the bijection term is well-established, it is time for Cantor's Diagonal Argument, to show that there could not be a bijection from the Natural numbers to the unit segment. I think this might just be the best 'party trick' to use when you want someone to get enthusiastic about set theory, though I find it necessary to talk a bit about bijections first.

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created May 7, 2020 at 12:11

Starting with some mind blowing paradoxes like asking the famous Russel's set paradox- does a set, that consists of all the sets that don't consist of themselves, consists of itself? (If it does - it doesn't, if it doesn't - it does).
Establishing the term of bijective functions, and with finite examples explain the motivation to define two equivalent sets as two that has a bijection between them.
A very cool and intuitive definition for an infinite set - a set which is equivalent to a strict subset of itself. It is nice to demonstrate with the Natural numbers and the Even numbers.
After the bijection term is well-established, it is time for Cantor's Diagonal Argument, to show that there could not be a bijection from the Natural numbers to the unit set. I think this is probably the best 'party trick' to use when you want someone to get enthusiastic about set theory, thought I find it necessary to talk a bit about bijections first.