The Sharp Mathematics Contest #1

in #steemstem7 years ago (edited)

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

gparadox-01.png

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.

Sort:  

Nice contest!
I'm looking forward for all the answers. I will write my own later, when I am home :)

they are the same since both sets go on until infinity and infinity isn't a real number, it cannot be defined. 2 times infinity is just infinity....infinity times infinity is also still just infinity....Just my 2 steem..

@eileenbeach has voted on behalf of @minnowpond. If you would like to recieve upvotes from minnowpond on all your posts, simply FOLLOW @minnowpond. To be Resteemed to 4k+ followers and upvoted heavier send 0.25SBD to @minnowpond with your posts url as the memo

The @OriginalWorks bot has determined this post by @tradersharpe to be original material and upvoted it!

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To call @OriginalWorks, simply reply to any post with @originalworks or !originalworks in your message!

To enter this post into the daily RESTEEM contest, upvote this comment! The user with the most upvotes on their @OriginalWorks comment will win!

For more information, Click Here! || Click here to participate in the @OriginalWorks writing contest!
Special thanks to @reggaemuffin for being a supporter! Vote him as a witness to help make Steemit a better place!

This post recieved an upvote from minnowpond. If you would like to recieve upvotes from minnowponds team on all your posts, simply FOLLOW @minnowpond.

    To receive an upvote send 0.25 SBD to @minnowpond with your posts url as the memo
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That is so wonderful. I am very grateful for that! Love it.

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