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PeroK's latest activity
PeroK
replied to the thread
Continuous functions on metric spaces
.
Do you see the close relationship between the proof of that theorem and the proof in this particular case?
May 18, 2024
PeroK
reacted to
pasmith's post
in the thread
Continuous functions on metric spaces
with
Like
.
You should start a new thread. Note that this new question is a generalization of the question you posted in this thread.
May 18, 2024
PeroK
replied to the thread
I
How to manipulate functions that are not explicitly given?
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You should definitely read my Insight!
May 18, 2024
PeroK
reacted to
Office_Shredder's post
in the thread
I
How to manipulate functions that are not explicitly given?
with
Like
.
Yeah, this is very abused notation. I think it helps to separate the variables a bit. Let ##f=f(x_1)##, and let ##x_1=y+\alpha \eta##...
May 18, 2024
PeroK
replied to the thread
I
How to manipulate functions that are not explicitly given?
.
That all seems fine, so I'm not sure where the problem lies. If you want a more in-depth discussion of multiple-variable partial...
May 18, 2024
PeroK
reacted to
Rick16's post
in the thread
I
How to manipulate functions that are not explicitly given?
with
Like
.
Here are two examples: The first one is from Taylor's Mechanics, section 6.2: Taylor takes the function ##f(y+\alpha\eta, y' +...
May 18, 2024
PeroK
reacted to
Ibix's post
in the thread
B
Falling into a black hole
with
Like
.
This isn't really correct. It's a result of taking the Schwarzschild time coordinate literally, which is a mistake similar to deciding...
May 18, 2024
PeroK
replied to the thread
B
Falling into a black hole
.
The first problem comes with the imprecise concept of "perspective". What does that even mean? It's true that light from a particular...
May 18, 2024
PeroK
replied to the thread
I
Manifold with boundary
.
There's no working model of the universe with a boundary.
May 18, 2024
PeroK
replied to the thread
Continuous functions on metric spaces
.
I'd like to see a simple proof in this case using that method. Or any proof, simple or otherwise, that isn't essentially just the...
May 17, 2024
PeroK
replied to the thread
Continuous functions on metric spaces
.
That's fine as far as it goes, but you really need a sound, logical proof. All ##\epsilon-\delta## proofs, in principle, should start...
May 17, 2024
PeroK
reacted to
Orodruin's post
in the thread
Continuous functions on metric spaces
with
Like
.
You want to find a ##\delta## such that if ##||f-g|| = \sup_{x \in I}|f(x)-g(x)| < \delta## then ##|\phi(f) - \phi(g)|< \varepsilon##...
May 17, 2024
PeroK
replied to the thread
Continuous functions on metric spaces
.
That all looks ill-conceived to me. For example, I don't think you've corrently identified the metric that is derived from the given...
May 17, 2024
PeroK
replied to the thread
Find the values of a and b to get max/min of certain expression
.
Here's an alternative approach. Note that we must have ##a, b < 0##. As both expressions are less in this case than for the equivalent...
May 17, 2024
PeroK
replied to the thread
Find the values of a and b to get max/min of certain expression
.
Trial and error is definitely precalculus.
May 16, 2024
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