What is the opposite of epsilon

[Pjpic]

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

 

[jedishrfu]

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

 

[Ssnow]

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 ...

 

[micromass]

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

 

[jedishrfu]

What does the H or N stand for?

 

[fresh_42]

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

 

[wrobel]

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

 

[beamie564]

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

.
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.