Recent content by Derek Hart

Yeah sorry I meant for both epsilon and the factorial to be in the denominator. Didn't even notice my mistake at first

I understand that the standard proof is a bit different from my own, but I want to know if my reasoning is valid. PROOF: Firstly, I assume that x is positive. I then consider p = inf{n∈ℕ : n>x} . In other words, I choose "p" to be the smallest natural number greater than x. If we choose n>p...

Think of it as the domino effect. You prove that the initial domino falls, and then if any domino falls, you show that the next one must fall as well, thus showing that every domino falls ultimately due to the "motion" of the first one. If that doesn't explain it clearly enough, think of the...

Homework Statement Give an example to show that the given "definition" of limx→aƒ(x) = L is incorrect. Definition: For each 0<δ there is an 0<ε such that if 0< l x-a I < δ , then I ƒ(x) - L I < ε . Homework EquationsThe Attempt at a Solution I considered the piece-wise function: ƒ(x) = (0 if...

Homework Statement I have been going through a textbook trying to solve some of of these with somewhat formal proofs. This is a former Putnam exam question. (Seemingly the easiest one I have attempted, which worries me). Consider a polynomial function ƒ with real coefficients having the...

That does seem simpler. Thanks

Alright, so to correct it I should just explicitly state that f is continuous at α?

Homework Statement Let A be a dense set**. Prove that if f is continuous and f(x) = 0 for all x in A, then f(x) = 0 for all x. **A dense set is defined, in the book, as a set which contains a point in every open interval, such as the set of all irrational or all rational numbers.Homework...

Ahh thanks, I feel stupid now. I haven't encountered the quadratic formula in any of the problems i have completed and haven't used it in a long time so it slipped my mind.

Homework Statement Decide whether the given function is bounded above or below on the given interval, and which take on their maximum or minimum value. (Notice that ƒ might have these properties even if ƒ is not continuous, and even if the interval** isn't closed) **The interval is (-a-1...

Dont try to improve your grades alone. You have resources such as your professor, and you should really have a heart to heart and show him or her that you have a passion for astronomy, but that you are struggling with the material. I guarantee you that your professor probably thinks you don't...

Thanks guys, i finally had an epiphany earlier today with your hints.

Probably not, since a universe emerging from absolute nothingness is a logical paradox within itself. I have always thought that since there is energy and matter now, there has to have always been some form of energy or physical information within the universe.

Homework Statement Find a formula for Σ(2i-1) = 1+3+5+...+(2n-1) Hint: What does the expression have to do with 1+2+3+...+2n? Homework EquationsThe Attempt at a Solution I have tried to solve this on my own for about a day now, and I am having trouble understanding the significance of the...