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

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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 '18 at 12:55

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## 2 Answers

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 '18 at 8:47

If it's a sequence of real numbers, then go ahead and start noting the first few terms. In your case it will be:

$$\frac{1}{2}, 1, \infty,-1, \frac{-1}{2},...$$

Is that really a sequence of real numbers? I'd say no, because $$\infty$$ is not a real number.