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The above symbol is referred to as ultimate equality in Tristan Needham's Visual Differential Geometry. How do I write it in latex?

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You can use \asymp to get $\asymp$ (for "is asymptotic to").

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A good resource is DeTeXify; you can draw the symbol you want and it will provide possible $\LaTeX$ codes for it. Note, however, that MathJax does not support all packages, so some of the options may not be available.

For this picture, it suggests \asymp, $\asymp$ as noted by Peter Phipps, which is regular $\LaTeX$ and so supported.

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