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Jul
22
revised Can $1=0$ ever make sense?
added 207 characters in body; edited title
Jul
22
comment Can $1=0$ ever make sense?
@JoshuaLaJeunesse indeed, I was trying to help :)
Jul
22
comment Can $1=0$ ever make sense?
@JoshuaLaJeunesse based on the comments so far (some demonstrating a negative answer, some a positive answer) you may wish to edit your question. It may assist in your question being re-opened.
Jul
22
comment Can $1=0$ ever make sense?
@Rahul but we do not make up rules. Instead we very carefully choose and pick very specific ones. Mathematics is a practice in which we can change the rules anytime we want, but we hardly ever do, and when we do it is out of compelling reasons to do so.
Jul
22
revised Can $1=0$ ever make sense?
edited tags
Jul
22
revised Can $1=0$ ever make sense?
edited tags
Jul
22
comment Can $1=0$ ever make sense?
It's a bit harsh to close this question so quickly. True, some more details are perhaps in order, but the question does make sense. I think we should be a bit more accommodating to questions spawned by curiosity that seems genuine. Moreover, the question has interesting answers.
Jul
21
answered Discrete mathematics, equivalence relations, functions.
Jul
20
comment What are some easy to understand applications of Banach Contraction Principle?
No offence @RobertLewis I'm just still puzzled by OP's comments here.
Jul
20
answered How can I use Banach Contraction Principle to solve $Ax = b$?
Jul
20
comment What are some easy to understand applications of Banach Contraction Principle?
@RobertLewis I suspect you are being sarcastic. Can you clarify on the Gauss business, in case I'm missing something?
Jul
20
comment What are some easy to understand applications of Banach Contraction Principle?
As I said, if you can find a metric for which $B$ is a contraction, then the sequence $B^n(y)$ converges to a solution, no matter what $y$ is. That's how you solve the original system of equations. Instead of computing the inverse, which can be very hard, all you need to do is compute $B$ again and again. With a bit of luck you also have some handle on the rate of convergence, and so you can determine how good a particular approximation to the solution is.
Jul
20
comment What are some easy to understand applications of Banach Contraction Principle?
@FemaleTank how do you propose to find $A^{-1}$? As I said, there are theoretical exact methods to solve systems of linear equations, but they are computationally hard. Having a simple iterative method that is guaranteed to converge to a solution is thus very helpful.
Jul
20
comment What are some easy to understand applications of Banach Contraction Principle?
@FemaleTank what are you talking about?
Jul
19
revised What are some easy to understand applications of Banach Contraction Principle?
edited body
Jul
19
answered What are some easy to understand applications of Banach Contraction Principle?
Jul
19
comment condition for a group to be abelian
@Yogi this wouldn't happen to be a homework problem? In any case, what have you tried? What are your thoughts on the matter?
Jul
19
comment Is the vector space of all linear transformations finite dimensional?
the fact that isomorphic vector spaces have the same dimension does not depend on finite dimensionality. It is a very straightforward proof. In fact, just prove that any monomorphism sends a linearly independent set to a linear independent set. That suffices for your purposes.
Jul
19
revised Is the vector space of all linear transformations finite dimensional?
edited tags
Jul
19
comment Is the vector space of all linear transformations finite dimensional?
You are probably assuming $V$ and $W$ are finite dimensional, otherwise the claim is false. Under this assumption, the isomorphism with the vector space of matrices is the standard one, and does not make any dimensionality assumptions on the space of transformations.