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I have a point $a$, with coordinates $(x,y,z)$ and I want to write, using set builder notation, that this point is found within the unit sphere $1=x^2 + y^2 + z^2$. How could I formulate this?

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    $\begingroup$ I question the (random) tag for this question $\endgroup$ – cdipaolo Aug 8 '18 at 20:55
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Almost exactly how you phrased it.

$$a\in\{(x,y,z)\in\mathbb{R}^3\;|\; x^2+y^2+z^2\leq1\}$$

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    $\begingroup$ Thank you, exactly what I was trying to find online $\endgroup$ – John Miller Aug 8 '18 at 20:42

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