The idea is that if you let then will be so small if is huge.
To show this use the following hint: and rationalize the numerator using the difference of two cubes formula.
how would i show that the set S = {cubed root(n+1) - cubed root(m) such that n,m are in N the natural numbers} is dense in the real numbers? the book says to use the fact that (cubed root(n+1) - cubed root(n)) is less than epsilon if n is greater than n0. i'm just in an elementary proof course. could anyone show me how to prove this? i would love some help.
how do you get it in the form to use the cubed root formula and why do you neutralize it?
yeah so basically the limit as it approaches infinity is zero, but how does that help me?
i don't know, all we've done in class is prove that the rational numbers are dense in the real numbers and the irrational numbers are dense in the real numbers. i don't see how to prove the density of this function based on what we did.
But of course that is clearly true. But does that have anything to do with the problem? Does it?
The question is to show that the given set is dense is the reals.
I have seen many such problems. BUT not this one.
Thinking about it for sometime, I now doubt that it is true.
To be dense, given a real number some element of the set must be “near” to that number.
Consider –7?