# What is the opposite of epsilon

• I
• Pjpic

#### Pjpic

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

I don't think there is a definitive term, I've seen people use these terms:
- immeasureable
- infinite

For every ##\varepsilon >0## ''very small'' you have ##\varepsilon^{-1}=\frac{1}{\varepsilon}## is ''very big'', in general there is no a preferred symbol to denote this ...

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

What does the H or N stand for?

Perhaps ##N## for number such as ##N(ε)##. I've also seen ##C## for a constant. But I've never seen a huge ##H##.

"The nightmare of mathematician is a sequence ##\varepsilon_n## that tends to infinity, as ##n \to 0##"
Paul Halmos

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