Math Is Fun Forum

Your attitude absolutely stinks, you're going to end up failing at everything you do if you won't admit your mistakes, especially when the counter-proof is staring you right in the face. Maybe in a thousand years when you finally grow up you'll be able to discuss some vaguely convtroversial maths, this is trivially obvious to anyone with a basic understanding of calculus.

Use the natural numbers as the group you're operating on, and only use operations that will form a group under the naturals

(Silly question)

Circular and fallacious

Just what exactly do you hope to gain by kidding yourself into thinking you're right? Or do you actually believe you're some enlightened high school child who understands everything on a level nobody else does? Get a clue, you haven't discovered something profound, in fact, you have to take at least an extra few steps to catch up with the rest of the muppets your age. It is YOUR logic that is backwards, and it is YOU that needs to start thinking. We can see your logic fails from outside it, you can't see it fails because you're stuck inside it and your little brain can't comprehend that it's circular.

They are the same value, with two real value decimal expansions.

I have a challenge for anybody reading this thread, find me somebody worse at maths than this guy.

It's the other way around, if you obtain a row of all zeros when it means one row was a linear combination of the other rows, hence not all rows are linearly independent. If this is true, then there will be infinitely many solutions to AX=0, because it will depend on less rows if you catch my drift. The number of rows of zeros is the kernel of the morphism, the number of non-zero rows is the rank.

http://en.wikipedia.org/wiki/Rank-nullity_theorem

That should help

Informally, if your kernel is zero (ie the morphism never fails injection), then the rank must be the length of the matrix, because all columns will be linearly independent and therefore the morphism will always be injective.

If you think about it

So they can't all be terms.

Actually he has a point, you should be constructing a tuple, not a set.

That is correct

...093844609550582231725359408238481117450...

16

What's wrong with, y'know, learning the definitions?