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Jul
22
answered Can $1=0$ ever make sense?
Jul
22
comment Can $1=0$ ever make sense?
@JoshuaLaJeunesse I edited your question further. I hope this is still in line with what you have/had in mind.
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
22
comment The trivial group, multiplication, 0 and 1
it's not clear what you are asking, particularly the remark about finiteness. Both groups you describe are finite, each having precisely one element. Generally, it would probably ease your understanding if you realize that you can construct a group structure on any set with single element. If that element is the number $1$ or the number $0$ is of no relevance. Continuity issues are also trivial for any single element group, as there is a unique topology on the set, and the group operations are automatically continuous.
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 How do you memorize theorems and techniques for long?
simple: do not memorise!