Real sequence

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Definition

A real sequence is the name given to a sequence, $(a_n)_{n\in\mathbb{N} }\subset\mathbb{R}$ - literally a sequence of real numbers - but where things like convergence are considered with the usual metric of the reals, that is:

• $d(x,y):\eq\vert x-y\vert$ - the absolute value of the difference between $x$ and $y$.

We can subtract $y$ from $x$ as the reals are a field.

References

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It should be obvious a real sequence is a sequence of reals!