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# The Proof is Trivial! watch

1. (Original post by Flauta)

Solution 425

Consider a trapezium with base 1, and two parallel sides of lengths 14 and 21. Its area is given by
How did you solve it so quickly??!
2. (Original post by Lord of the Flies)
How did you solve it so quickly??!
My little secret.
3. (Original post by Lord of the Flies)
How did you solve it so quickly??!

I would've used the Hardy-Littlewood inequality to solve it. I'm surprised at his geometric approach though.
4. (Original post by Zakee)
I would've used the Hardy-Littlewood inequality to solve it. I'm surprised at his geometric approach though.
Why surprised?

There can be more than one proof, why don't you post yours?
5. (Original post by Lord of the Flies)
Problem 425*/**/***

Evaluate
Let B be a topological algebra with continuous trace , then, it's clear that:

.

(Consider wedge products and that r is a cyclic action over the symmetry group mapped out by .)

Substitute p=7, and evaluate. Voila.
6. Problem426***

Evaluate

and deduce what was going through my mind when I thought of this question.
7. (Original post by MW24595)
Let B be a topological algebra with continuous trace , then, it's clear that:

.

(Consider wedge products and that r is a cyclic action over the symmetry group mapped out by .)

Substitute p=7, and evaluate. Voila.
Did you just string together a load of random mathy things, or is that actually a genuine formula?
8. (Original post by james22)
Did you just string together a load of random mathy things, or is that actually a genuine formula?
I was just typing out a proof. Give me a moment, my dear friend!
9. (Original post by james22)
Problem426***

Evaluate

and deduce what was going through my mind when I thought of this question.
Damn, that question's too hard for me but I'm guessing it's the number of presents you're hoping for Christmas?
10. (Original post by Zakee)
I'm currently in year 13, and I think it may be University level, I'm not sure. I heard from someone that it comes up in FP3 (A-level), but I haven't studied FP3 yet. I'm just extremely interested in Pure Mathematics and have a knack for problem-solving.
Almost finished FP3- it definitely does not come up.
11. (Original post by Flauta)
Damn, that question's too hard for me but I'm guessing it's the number of presents you're hoping for Christmas?
Nope.

The number of presents I am hoping for it actually .
12. (Original post by nahomyemane778)
Almost finished FP3- it definitely does not come up.
Are you on the mickey mouse exam board or something?
13. (Original post by james22)
Nope.

The number of presents I am hoping for it actually .
Last year I got 37 so I'm hoping for 38 this time around
14. (Original post by Lord of the Flies)
Problem 425*/**/***

Evaluate
The solutions posted so far are good, but I will use a different approach.

Firstly, it's obvious by the finiteness of (Zhang, 2013) that the integral is well defined.

It is left to calculate its value. Consider an algebra A over an 4k-dimensional Hyperkahler manifold as . Then it is possible to construct a Banach space X such that every operator on the space is close to an operator of A. (Gowers, Maurey, 1994).

Thence is follows that
15. (Original post by nahomyemane778)
Almost finished FP3- it definitely does not come up.
Wait what?! You don't have the Bertrand-Chebyshev?! O.o What about the Hardy-Littlewood?
16. (Original post by Flauta)
Last year I got 37 so I'm hoping for 38 this time around
17. (Original post by Lord of the Flies)
Are you on the mickey mouse exam board or something?

Im on edexcel. Am I in a dream world? Why the hell would Bertrand's Postulate appear in FP3?
18. (Original post by MW24595)
Let B be a topological algebra with continuous trace , then, it's clear that:

.

(Consider wedge products and that r is a cyclic action over the symmetry group mapped out by .)

Substitute p=7, and evaluate. Voila.
(Original post by james22)
Did you just string together a load of random mathy things, or is that actually a genuine formula?
I realized it wasn't all that obvious. So, I decided to elaborate a little. The proof is nothing too extraordinary, but it does make some delightfully intricate use of symmetry.

Consider that:

Now, recall that r is the cyclic action on the permutation group Sp defined by
and Clearly , and . Since p is odd, . And so we have our trace. Moving to the first in every product, we are done.

From here on, the proof is trivial.
19. (Original post by und)
The solutions posted so far are good, but I will use a different approach.

Firstly, it's obvious by the finiteness of (Zhang, 2013) that the integral is well defined.

It is left to calculate its value. Consider an algebra A over an 4k-dimensional Hyperkahler manifold as . Then it is possible to construct a Banach space X such that every operator on the space is close to an operator of A. (Gowers, Maurey, 1994).

Thence is follows that
I don't quite understand the statement "4k-dimensional Hyperkahler manifold", since all Hyperkahler manifolds have dimension 4k. It's like me saying "consider an associative group".
20. (Original post by james22)
I don't quite understand the statement "4k-dimensional Hyperkahler manifold", since all Hyperkahler manifolds have dimension 4k. It's like me saying "consider an associative group".
That's just to help increase clarity. Otherwise could refer to absolutely anything.

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Updated: February 22, 2018
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