Question about ordered pairs...

Say you have the ordered pair A=((a,b),c), where (a,b) is itself an ordered pair. Would it correct to say that A=(a,b,c)?

It would generally not be correct.

(a,b,c) is an ordered triplett
while
( (a,b),c )

is an ordered pair that demontrates a pairing of
the number c with the ordered pair (a,b)

It is possible to construct a one to one
AND onto correspondance
between the ordered pairs
R²→ R represented by ( (a,b),c )
and the ordered triplets of
R³ represented by (a,b,c)

and then we could say each element of
the first set in R²→ R is represented by
the elements of R­³

That is frequently done in multivariable calculus where

z = f(x,y) is graphed in R³ although f is
literally a function from R² to R .


Note that we are doing the same thing in ordinary math
when we have a function

y=f(x)

the function is from R to R but we graph it in R X R = R²

So answer in general to your question is no, but when considering
functions

z =f(x,y) you end up with each (x,y), f(x,y) correponding to (x,y,z)

Note that two ordered pairs (x, y) and (u, v) are equal if and only if x = u and y = v. In your case, ((a,b), c) = (a,b,c) if and only if (a,b) = a. But this is not true since ((a,b),c) has two coordinates while (a,b,c) has three. Furthermore, associativity only applies to binary operations such as addition [i.e. (2+3)+4 = 2+(3+4) = 2+3+4 = 9]. This is not true of ordered pairs

An n-tuple simply says that n things are placed in a specific order. In this sense, what you say seems to be correct.

no.thats wrong
thats two pairs
one is (a,b). Another ((a,b), c)
so we cant say that