MHB Can someone help me in the right direction with this proof

Thread starter WJMeyer
Start date Jul 13, 2020
Tags

Direction Proof

AI Thread Summary

A 1001x1001 square table is filled with the numbers 1 to 1001, ensuring each number appears in every row and column. The table is symmetric with respect to one of its diagonals. The discussion revolves around proving that all numbers from 1 to 1001 must appear along this diagonal. The original poster initially sought help but later indicated they solved the problem independently. This highlights the importance of symmetry in mathematical proofs related to structured arrangements.

Jul 13, 2020

WJMeyer

A square table of size 1001x1001 is filled with the numbers 1; 2; 3; ... ; 1001 in such a way that in every row
and every column all those numbers appear. If the table is symmetric with respect to one of its diagonals,
prove that in this diagonal all of the numbers 1; 2; 3; ... ; 1001 appear.

Mathematics news on Phys.org

Jul 13, 2020

WJMeyer

Nevermind I got it:)

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...

View full post »

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...

View full post »