Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 0 down vote favorite

Let $1<b\in \mathbb{R}$ and $y\in \mathbb{R}$. I have proved that $A=\{x\in \mathbb{R}\mid b^x < y\}$ is nonempty when $y > 1$. Please give me any hint how to show that $A$ is nonempty when $y\leq 1$.

share|improve this question
It depends on your definition of $b^x$ – Norbert Jul 9 '12 at 20:44
I want to delete this post.. – Katlus Jul 9 '12 at 20:47
$x<0$ basically lets you convert $b$ to $1/b$ and use your previous proof. – gt6989b Jul 9 '12 at 20:50
If $y = 1$, there won't be $x \in \mathbb{R}$ s.t. $b^{x}<1$ for $b=1$. – m.woj Jul 9 '12 at 20:53
@Katlus: Is there not a "delete" link in the bottom left of your post (by "link," "edit," etc.)? – Jonas Meyer Jul 10 '12 at 14:10

1 Answer

up vote 0 down vote accepted

Consider the sequences $x_n=-n$ and $b_n = b^{x_n}$. Ask what the limit of $b_n$ is and use facts about limits.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.