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1) we use letters in mathematics to represent any element of a set. So

this letter (for example "x") is any element of a specific set and we call

it a variable. We can substitute it with any specific element of the set

(for example in functions) and we can also apply any properties that the

elements of this set have to expressions that contain this variable (for

example if x is a real variable then 3*x+4*x=(3+4)*x=7*x ).

2) we use letters when we refer to specific elements of a set that we just

don`t know ,don`t care which are they or that we are looking for ( in that

case they are called "unknown" ) . Also when we generally want to refer to

any element of a set, considering however that it is constant in every

specific case ( to make it more clear: f(x)=3*x+b x can vary but b is

considered a constant-however for the various values of b different

functions occur).

As you see, until now there`s no question . I think all these are correct

but want you to check these and correct any mistakes. Something to add:

when we say that a(bc)=(ab)c with a,b,c real numbers , a,b,c represent any

real number right? Are they variables? Also when we say that "if f is

continuous in [a,b] and f(a)f(b)<0 then there`s at least one j with

a<j<b and f(j)=0 (with a<b)" we mean that a,b can be any real

number with a<b but of course they are constants, right? I mean we

cannot put any value in the place of a,b so they are actually specific

numbers, but we use letters to show that in any (specific and defined) set

[a,b] we can apply this theorem?

Are there any other cases of using letters in mathematics?

Thanks