Hey people! Just for fun, I have decided to organise a mathematics contest. The prizes, from my own Steem wallet, are:-
Prizes
1st Prize: 5 SBD
2nd Prize: 3 SBD
3rd Prize: 2 SBD
If I get sponsors, then the prizes may be increased.
The Puzzle
Alice and Betty are arguing over the set P of all positive whole numbers, and the set E of all positive even numbers.
Alice says: "P has more numbers than E, because for example, 3 is in the set P, but it is not in set E."
Betty says: "No! P has the same number of elements as E. The elements in P can be paired up with the elements in E."
Alice says: "But but but but but E contains only numbers like 2, 4, 6, 8, 10, 12, 14, and the number 3 is not in there, whereas P contains numbers like 1, 2, 3, 4, 5, 6, 7, 8, 9, blah blah blah to 14, so P has more elements."
Betty says: "No! No! No! No! No! The blah blah blah goes on forever. Do you see the three dots (...) thingy? the ellipses for both sets? Every positive whole number can be paired with a positive even number by multiplying with 2 ... So P and E has the same number of elements."
Who is / are correct? Can you explain how / why?
Criteria
I will be judging the entries for the competition based on the following criteria:-
(1) rigour and logic
(2) explanation of the mathematical concepts involved
(3) if you can tell the story or history related to this puzzle, that would be even better.
How to Join the Competition
To participate in this competiton, you must do all of the following:-
(1) upvote this post
(2) resteem this post
(3) follow me @tradersharpe
(4) write your own post on Steemit
(5) reply below to this post with a link to your post
Deadline
Please submit your entry to this contest at or before 23:59 GMT, Sunday, 8th October 2017.
All the best!
@tradersharpe
-- promoting sharp minds
Winners' announcement here.