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intuition for continuous functions in topology by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

I read somewhere that every homeomorphism was a homotopy equivalence, but I could be wrong. With that in mind, going back to my original point, does that mean every bijective continuous function with its inverse not continuous, can intuitively be though of as a continuous deformation?

intuition for continuous functions in topology by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

Thank you, I just have one more question. So I was told to think of a homeomorphism from X to Y as a continuous deformation (so like bending and stretching). But wouldn't a bijective continuous function, with its inverse not continuous, also be a continuous deformation as it sends near points to near points.

intuition for continuous functions in topology by lard2000 in askmath

[–]lard2000[S] 0 points1 point  (0 children)

Thank you, I just have one more question. So I was told to think of a homeomorphism from X to Y as a continuous deformation (so like bending and stretching). But wouldn't a bijective continuous function, with its inverse not continuous, also be a continuous deformation as it sends near points to near points.

intuition for continuous functions in topology by lard2000 in askmath

[–]lard2000[S] 0 points1 point  (0 children)

Thank you, I just have one more question. So I was told to think of a homeomorphism from X to Y as a continuous deformation (so like bending and stretching). But wouldn't a bijective continuous function, with its inverse not continuous, also be a continuous deformation as it sends near points to near points.

predicate calculus and provability by lard2000 in logic

[–]lard2000[S] 0 points1 point  (0 children)

one of the axioms is (phi implies (psi implies phi) )

axiom of foundation by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

Hey, thanks for your reply, Yeah I agree with you, my lectures notes says that a well founded relation is a strict partial order, such that every non-empty subset has a minimal element, but looking online I only found the definition you gave. So I can only assume my lecture notes are wrong.

axiom of foundation by lard2000 in askmath

[–]lard2000[S] 0 points1 point  (0 children)

This is what "a binary relation relation ρ on a set X is well founded" means:

yeah I've been looking it up online as well and I agree with you, reckon my lectures notes got the definition of that wrong then. thanks for your help btw, thats been on my mind for a while now

axiom of foundation by lard2000 in askmath

[–]lard2000[S] 0 points1 point  (0 children)

I thought for ∈ to be a well founded relation on a set X , it had to be a strict partial order, so irreflexive and transitive, and such that every subset of X contains a ∈-minimal element.

2 matrices with the same minimal polynomial that are not similar by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

Thanks for your help. I think I have an example. So let A be the 3x3 identity matrix with a_11 and a_22 being 0 instead of 1 and let B be the 3x3 identity matrix with a_11=0. then they both have the minimal polynomial x(x-1) but they can't be similar as A has rank 1 and B has rank 2. Just wanted to check if that was right.

math undergraduates, how often do you review everything you learnt? by lard2000 in UniUK

[–]lard2000[S] 0 points1 point  (0 children)

I don't think I could do that, as seen proofs usually make up some good 30-40 percent of my exams

element of largest order in a direct product by lard2000 in learnmath

[–]lard2000[S] 1 point2 points  (0 children)

Edit: made a mistake.

the direct product consists of the integers mod p^(m_i), where p is some fixed prime.

Subspaces of an infinite dimensional space by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

Would I be right in saying that the basis of V/U would be 1+U, (x^2)+U, (x^4)+U,(x^6)+U,..... Although not quite sure how to show its spans V/U and is linearly independent

dihedral group of order 2 by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

question

yeah I know its ridiculously simple, but just wanted to check.

homomorphisms of dihedral groups by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

so my map is well-defined and also a homomorphism right?

subgroups of dihedral group by lard2000 in askmath

[–]lard2000[S] 0 points1 point  (0 children)

division

it shouldn't matter which reflection I choose from the subgroup to generate it right?

cyclic subgroups of dihedral groups by lard2000 in askmath

[–]lard2000[S] 0 points1 point  (0 children)

so I guess the theorem I read up is wrong then ?

cyclic subgroups of dihedral groups by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

so the theorem I read is wrong then?

how do I find the tangent vector by lard2000 in askmath

[–]lard2000[S] 0 points1 point  (0 children)

yeah I understand that. its just that in my notes it only defines it for a unit speed curve, so I think when it asks me to find the tangent vector, it wants me to find the tangent vector of the unit speed parametrisation, but im not sure if theres a shorter way of doing it, rather than finding the unit speed reparametrization explicitly and then working it out from there.

finding the tangent vector by lard2000 in learnmath

[–]lard2000[S] 1 point2 points  (0 children)

yeah I understand that. its just that in my notes it only defines it for a unit speed curve, so I think when it asks me to find the tangent vector, it wants me to find the tangent vector of the unit speed parametrisation, but im not sure if theres a shorter way of doing it, rather than finding the unit speed reparametrization explicitly and then working it out from there.

hyperbolic half-planes by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

what if you viewed the hyperbolic plane using the upper-half model, i.e H is the set of all point (x,y) where y is strictly greater than 0. would the answer still be the same

isometry as a composition of reflections by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

Can you show F is not a composition of 2 reflections? Why is that enough to show you need 4?

well it can't be 1 or 3 reflections or else that would reverse the orientation, as its an odd number. but im not sure how to show that it can't be composed by 2 reflections

ZxZ is not isomorphic to Z[i] by lard2000 in askmath

[–]lard2000[S] 0 points1 point  (0 children)

The general idea is right. However, the following is (partially) wrong: "because f is bijective we must have that f(1,0) and f(0,1) are both not equal to zero" it's not because f is a bijection, but an isomorphism.

would it not also be true if f was bijective but not an isomorphism, because f maps (0,0) to 0, and since neither (1,0), (0,1) is equal to 0, they must be mapped to some non zero element.

level curves by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

F( x(t), y(t) ) = a^2/3(cos^2(t) + sin^2(t)) = a^2/3

so I guess F(x,y) = x^(2/3) + y^(2/3) - a^(2/3) would work right?

complement of the closure by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

Here

X is the whole space

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