All Questions
Tagged with real-numbers proof-writing
127
questions
0
votes
3
answers
381
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Having trouble understanding Cantors proof that real numbers are uncountable
I found this video very easy to follow and understood the proof.
https://www.youtube.com/watch?v=mEEM_dLWY0g
However, I am still having trouble understanding the proof presented to me in my csmath ...
- 25
2
votes
1
answer
398
views
My first proof employing the pigeonhole principle / dirichlet's box principle - very simple theorem on real numbers. Please mark/grade.
What do you think about my first proof employing the pigeonhole principle? What mark/grade would you give me? Besides, I am curious about whether you like the style.
Theorem
Among three elements of ...
- 1,321
3
votes
0
answers
190
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My first simple direct proof (very simple theorem on real numbers). Please mark/grade.
What do you think about my first simple direct proof? What mark/grade would you give me? Besides, I am curious about whether you like the style.
Theorem
Let $I = [a,b]$ be a non-empty closed ...
- 1,321
1
vote
1
answer
125
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Possible book correction or am I missing something?
Hi I am teaching myself analysis and bought "Analysis - With an introduction to Proof" by Steven R. Lay. Now one of the practice problems is "Determine the truth value of each statement, assuming x, y ...
- 825
3
votes
3
answers
467
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Formal proof of: $x>y$ and $b>0$ implies $bx>by$?
Property: If $x,y,b \in \mathbb{R}$ and $x>y$ and $b>0$, then $bx>by$.
What is a formal (low-level) proof of this result? Or is this property taken as axiomatic?
The motivation for this ...
0
votes
1
answer
82
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Math proof involving open and closed intervals
So this is a multipart question, and I have a couple "theories" on how to attack it but still stuck in the infancy stages. Basically, not very far.
For each real $r>0$ let $I_r$ denote the open ...
- 85
5
votes
1
answer
6k
views
For every $\epsilon >0$ , if $a+\epsilon >b$ , can we conclude $a>b$?
If $a+\epsilon > b$ for each $\epsilon >0$, can we conclude that $a>b$?
Please help me to clarify the above. Thanks in advance.
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