# Can a sequence be undefined at a point? [duplicate]

This question already has an answer here:

A sequence which is a mapping from $$\mathbb{N} \to \mathbb{R}$$.

For example can the sequence $$\{a_n\} = 1/(3-n)$$. This would be undefined at $$3$$. Is it a sequence?

## marked as duplicate by Brahadeesh, drhab, Hans Lundmark, Lord Shark the Unknown, user10354138Nov 17 at 12:55

If you define a sequence as a mapping $$f$$ from $$\Bbb N$$ to $$\Bbb R$$, then no, a sequence cannot be undefined at a point $$x$$, since if $$f(x)$$ was not defined, then $$f$$ isn't a mapping.
• +1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $\frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up. – Dave L. Renfro Nov 17 at 8:47
$$\frac{1}{2}, 1, \infty,-1, \frac{-1}{2},...$$
Is that really a sequence of real numbers? I'd say no, because $$\infty$$ is not a real number.