Question

is a sequence a function whose domain is a set of real numbers? I know it's a set of natural numbers. Are natural numbers and real numbers the same thing?

Answer 1

natural numbers are \(1,2,3,...\) although some people include \(0\), a debate that i don't enter in to

Answer 2

real numbers are everything, unless you enter the world of complex numbers

Answer 3

a sequence is usually written as
\[a_1,a_2,a_3,...\] but it is in fact a function of natural numbers if you write is as \[a(1),a(2),a(3),...\]

Answer 4

So, the answer would be no?

Answer 5

there are many, many, MANY more real numbers than natural numbers. the real numbers contain infinitely many "copies" of the natural numbers, in fact!

Answer 6

a sequence is a natural number that maps from the natural numbers to real numbers (for your purposes): $$a:\mathbb{N}\to\mathbb{R}$$i.e. it takes natural number indices and maps them to values in the sequence

Answer 7

So, a sequence is a function whose domain is a set of natural numbers and /not/ real numbers?

Answer 8

the domain is typically taken to be the natural numbers, yes