All Questions
3
questions
0
votes
1
answer
22
views
How to more formally prove this inequality
This is a simple problem I came up with while doing another problem:
Given: $n < (n + \frac{1}{2}) < y < (n + 1)$
Prove: $|y - n| > |y - (n + 1)|$
So how I proved it was simply using the ...
0
votes
2
answers
2k
views
Absolute Value Proof By Cases
I'm currently working through D. Velleman's How to Prove it. I have a question regarding an absolute value proof by cases (#10; section 3.5).
The question asked is to prove that:
$$
\forall x\in\...
1
vote
1
answer
54
views
My proof of: $|x - y| < \varepsilon \Leftrightarrow y - \varepsilon < x < y + \varepsilon$
Is it reasonable to prove the following (trivial) theorem?
If yes, is there a better way to do it?
Let $x, y \in \mathbb{R}$.
Let $\varepsilon \in \mathbb{R}$ with $\varepsilon > 0$.
$\textbf{...