What is the opposite of epsilon

  • #1
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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?
 

Answers and Replies

  • #2
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I don't think there is a definitive term, I've seen people use these terms:
- immeasureable
- infinite
 
  • #3
Ssnow
Gold Member
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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 ...
 
  • #4
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Usually, people like to use capital letters for this, such as ##H## or ##N##.
 
  • #5
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What does the H or N stand for?
 
  • #6
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Perhaps ##N## for number such as ##N(ε)##. I've also seen ##C## for a constant. But I've never seen a huge ##H##.
 
  • #7
"The nightmare of mathematician is a sequence ##\varepsilon_n## that tends to infinity, as ##n \to 0##"
Paul Halmos
 
  • #8
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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.
 

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