Recent content by ekko

If I pick epsilon = |f(x)-g(x)|/2 then that would help me show that the set |f(x):f(x) is not equal to g(x)| is open; and then can I just say that because f and g are continuous the inverse image set |x:f(x) is not equal to g(x)| is open? Which theorem says that the inverse of an open set is open?

That makes sense, but how do I show that the set where f(x) is not equal to g(x) is open?

Homework Statement Suppose f: [a,b] -> R and g: [a,b] -> R are both continuous. Let T = {x: f(x)=g(x)}. Prove that T is closed. Homework Equations If a function f: D -> R is continuous, then for each E > 0 there exists a delta >0 such that if |x-x0| < delta (for x, x0 in D) then...

i still don't get it. i don't know which estimates to use to make the proof work. i have to get from (n+1)^2 + 3 < ... <= ... <= ... 2*(n^2) +1 < 2^(n+1) +5. one thing i can do is expand this to n^2 + 2n +1 + 3 < ... n^2 + n^2 + 2n +4 < 2*(n^2) +2n +4, but how is that last term less than or...

ok well for 1) i first state that 1^2 +3 = 4 and 2^1 + 5 = 7, so 4 < 7. Therefore the statement is true for n = 1. then i assume that for some natural number n, n^2 +3 < 2^n + 5, and i have to prove from this that (n+1)^2 +3 < 2^(n+1) + 5. so first i multiplied both sides by 2 (which doesn't...

hello, i am having some trouble with a few induction problems. 1) Prove by induction that for all natural numbers n, n^2 + 3 < 2^n + 5. 2) Prove by induction that for all natural numbers n, (1-1/2)(1-1/4)...(1-1/(2^n)) > or equal to 1/4 + 1/(2^(n+1)). i got started on these but ran into...