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## Main Question or Discussion Point

Is there a notation for the opposite of epsilon (infinitesimal) in the way that infinity is the opposite of zero?

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Is there a notation for the opposite of epsilon (infinitesimal) in the way that infinity is the opposite of zero?

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jedishrfu

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Ssnow

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Usually, people like to use capital letters for this, such as ##H## or ##N##.

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jedishrfu

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What does the H or N stand for?

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fresh_42

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Paul Halmos

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The opposite of infinity is not zero, it's ##\varepsilon##.Is there a notation for the opposite of epsilon (infinitesimal) in the way that infinity is the opposite of zero?

Source : This Numberphile video

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Depends how you define "opposite". If you mean additive inverse, then ##-\infty## would be the opposite of ##\infty##, and ##-\varepsilon## for ##\varepsilon##. If by "opposite" you mean multiplicative inverse, then the opposite of ##\varepsilon## would be ##\infty##. Zero, on the other hand doesn't have a multiplicative inverse, so maybe we can say it doesn't have an opposite.

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