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issacnewton's latest activity
I
issacnewton
posted the thread
Problem involving recursion theorem
in
Calculus and Beyond Homework Help
.
Now, we are given that ##\mathbb{N}'## is a set and ##1' \in \mathbb{N}'## and ##s' :\mathbb{N}' \rightarrow \mathbb{N}' ## is a...
Yesterday, 8:04 AM
I
issacnewton
reacted to
mathwonk's post
in the thread
Proving well ordering principle from Peano Axioms
with
Like
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quantifiers are actually essential for precise statements. recall existential quantifiers affirm a statement for at least one element...
Friday, 12:50 PM
I
issacnewton
replied to the thread
Proving well ordering principle from Peano Axioms
.
Awesome !!. I had studied the book "How to Prove It: A Structured Approach" by Daniel Velleman. He is a set theorist, so the language of...
Friday, 1:30 AM
I
issacnewton
reacted to
mathwonk's post
in the thread
Proving well ordering principle from Peano Axioms
with
Like
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Excellent, except to be picky, you have omitted some existential quantifiers, e.g. in line minus 17, it should say "there exists h such...
Friday, 1:26 AM
I
issacnewton
reacted to
mathwonk's post
in the thread
Proving well ordering principle from Peano Axioms
with
Like
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If it makes you feel any better, I am a retired professional mathematician, and although I can follow that proof, I think it is one of...
May 1, 2024
I
issacnewton
replied to the thread
Proving well ordering principle from Peano Axioms
.
Ok. I think I can put your arguments together and following is my proof. Let ##H## be defined as follows $$H = \Bigl\{a \in \mathbb{N}...
May 1, 2024
I
issacnewton
replied to the thread
Proving well ordering principle from Peano Axioms
.
Thanks.
Apr 10, 2024
I
issacnewton
reacted to
FactChecker's post
in the thread
Proving well ordering principle from Peano Axioms
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.
##H \subseteq \mathbb{N}## is the set of all possible lower limits for the set ##G##. For a proof by contradiction, it was assumed that...
Apr 10, 2024
I
issacnewton
posted the thread
Proving well ordering principle from Peano Axioms
in
Calculus and Beyond Homework Help
.
I am trying to understand the proof given in Ethan Bloch's book "The real numbers and real analysis". I am posting snapshot of the proof...
Apr 10, 2024
I
issacnewton
replied to the thread
Prove if ##a\cdot c = b \cdot c## then ##a = b## using Peano postulates
.
Thanks nuuskur. If I write many equations like (1) and (2), it will take lot of space and I may not get any responses.
Mar 17, 2024
I
issacnewton
reacted to
nuuskur's post
in the thread
Prove if ##a\cdot c = b \cdot c## then ##a = b## using Peano postulates
with
Like
.
You could save so much space and the reader's (and your own) sanity by writing things more concisely. Show by induction on...
Mar 17, 2024
I
issacnewton
posted the thread
Prove if ##a\cdot c = b \cdot c## then ##a = b## using Peano postulates
in
Calculus and Beyond Homework Help
.
with this background, we proceed to the proof. Let us define a set $$ G = \{ x \in \mathbb{N} | \; y, z \in \mathbb{N}\; \text{ if }...
Mar 15, 2024
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