Hi, everyone.
Last time this question was asked 4 years ago.
I believe it is possible to generate even greater answers.
Thanks in advance.
In: Mathematics
There is no concrete or universally accepted definition. But generally the term Space is used when referring to a collection of something in the universe.
For example, all matrices which have the dimensions of 2×2 would be in one space, and matrices with dimensions of 10×10 would be in another space, since a 2×2 matrix and a 10×10 matrix share different dimensions and makes them unique in that way.
It’s a very general term, and a space is not always used in mathematics.
That’s just how it is called. We associate different characteristics with spaces and, let’s say, fields. If we flip the name, nothing happens. The meaning is important
a “space” is usually a “set” with a certain structure. A vector space is a set (of vectors), for which certain linear relations hold. A metric space is a set were some kind of distance is defined….
Of course the imprinted structure is kind of arbitrary, but certain simple structures (like the above) give rise to very rich relations (and applications).
It refers to the set from which solutions to a given type of problem are drawn from.
If you are trying to factor a large integer, you could work in integer space, and that would allow you to ignore irrational and fractional numbers because by definition they can’t be solutions. You could further narrow your solution space down to positive integers and eventually to prime numbers. You may even to do some math and prove only certain kinds of prime numbers are possible factors.
That applies to many areas of math and science. You start with a space of all possible solutions, and start chipping away at it until you whittle it down to a manageable size.
Latest Answers