# The Sharp Mathematics Contest #1

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.

beachhermit (50)7 years agoHi @tradersharpe.

I love maths too!

And I love contests.

My entry is at https://steemit.com/mathematics/@beachhermit/maths-makes-me-happy-a-maths-competition-even-happier

Good luck to everyone.

grandrey (40)7 years agoI love maths.Do you?

resorus (47)7 years agoNice contest!

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

resorus (47)7 years agoHere it is! :-)

https://steemit.com/mathematics/@resorus/which-set-is-bigger-p-or-e

falsefreedom (41)7 years agothey 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..

minnowpond (62)7 years ago@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

minnowbooster (73)7 years ago**@tradersharpe got you a $6.58 @minnowbooster upgoat, nice!

Want a boost? Minnowbooster's got your back!

originalworks (69)7 years agoThe @OriginalWorks bot has determined this post by @tradersharpe to be original material and upvoted it!

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

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minnowpond (62)7 years agoThis post recieved an upvote from minnowpond. If you would like to recieve upvotes from minnowponds team on all your posts, simply FOLLOW @minnowpond.

aborjin (-2)(1) 7 years agoThat is so wonderful. I am very grateful for that! Love it.