1
$\begingroup$

My text tells me that the general term of a sequence can be looked at like a function:

$ f:\mathbb{N}\rightarrow \mathbb{R} $

What does that mean translated into common english?

$\endgroup$
2
$\begingroup$

This specific case is called a sequence. The function $f$ takes in an input from the natural numbers (denoted $\mathbb N$), and gives an output in the real numbers (denoted $\mathbb R$).

In general, this notation contains three parts: the function name, the domain, and the codomain. The function name (in your case $f$) is the same $f$ appearing in the notation $f(x)$. The domain is the set of inputs to your function (in your case the natural numbers $\mathbb N$). The codomain is the set of possible outputs that the function can give (in your case the real number $\mathbb R$).

$\endgroup$
  • $\begingroup$ In high school I learned about the range of the function. How is that related to the codomain? $\endgroup$ – User1996 Sep 7 '14 at 18:30
  • $\begingroup$ The range will typically be a subset of the codomain. The elements of the range are the values that are mapped to. For instance, you could define $f:\mathbb R \to \mathbb R$, $f(x) = 12$. The codomain of your function is $\mathbb R$, but the range is just $\{12\}$. $\endgroup$ – theage Sep 7 '14 at 18:32
  • $\begingroup$ Ah I see, so the codomain is the family of numbers that the range belongs to? $\endgroup$ – User1996 Sep 7 '14 at 18:35
  • $\begingroup$ Exactly!${}{}{}$ $\endgroup$ – theage Sep 7 '14 at 18:37

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.