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Tagged with real-numbers proof-writing
127
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Help with 2 questions my professor gave us
I was wondering how to solve these two proofs my professor put on the blackboard today. He said they were pretty easy but i'm still unsure how to prove them. ANy help would be greatly appreciated!
(i)...
CommunityBot
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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 ...
CommunityBot
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Help solving a proof
My professor put this up on the blackboard and I was wondering how to solve it.
Let $x,y \in \mathbb{R}$. Then |$x$|< |$y$| if and only if $x^2 < y^2$.
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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 ...
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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 ...
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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 ...
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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 ...
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