Recent content by vinnie

or maybe we're supposed to prove the conjecture false by counterexample... using 6 and 8 perhaps.

There is an error.

or are you saying we don't need the negation, just provide 4 and 6 as counterexamples and be finished...?

we assume the negation of the conjecture. which is for all natural numbers, a and b, if a and b are both even, then (a^2 +b^2) IS a perfect square. if we use 4 and 6 as counterexamples we do not get a perfect square, so we have a contradiction...

a counterexample in the negation of the conjecture.

true, but using four and six as counterexamples...

so I set up the negation, then we assume a and b are even and that a^2 +b^2 is a perfect square. Then subbing 4 for a and 6 for b, we get a contradiction?

Homework Statement For all natural numbers, a and b, if a and b are both even, then (a^2+b^2) is not a perfect square. (prove this) Homework Equations The Attempt at a Solution I tried proving by contradiction and got (2s)^2 +(2t)^2 =k^2. which translates to 4s^2 +4t^2=k^2. I...

That sounds encouraging. how were your abstract algebra and analysis classes when you took them?

It appears they are using Gordon's Real Analysis: A first course.

it's allowed/possible at my school... as long as the prereqs are met. What about the other two classes? How many hours for each of those?

simultaneously. Can it be done? How many hours are spent outside of class in each subject?

I was speaking of the second part of the test. I know all about the first part. Thank you.

Now that I know about (-1)^n, I know it's not applicable.

so we would take the limit of 1/2srqrt(3n)? how would we find the sum of this infinite series?