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I What is the opposite of epsilon

  1. Jun 10, 2016 #1
    Is there a notation for the opposite of epsilon (infinitesimal) in the way that infinity is the opposite of zero?
     
  2. jcsd
  3. Jun 10, 2016 #2

    jedishrfu

    Staff: Mentor

    I don't think there is a definitive term, I've seen people use these terms:
    - immeasureable
    - infinite
     
  4. Jun 10, 2016 #3

    Ssnow

    User Avatar
    Gold Member

    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 ...
     
  5. Jun 10, 2016 #4
    Usually, people like to use capital letters for this, such as ##H## or ##N##.
     
  6. Jun 10, 2016 #5

    jedishrfu

    Staff: Mentor

    What does the H or N stand for?
     
  7. Jun 10, 2016 #6

    fresh_42

    User Avatar
    2017 Award

    Staff: Mentor

    Perhaps ##N## for number such as ##N(ε)##. I've also seen ##C## for a constant. But I've never seen a huge ##H##.
     
  8. Jun 10, 2016 #7
    "The nightmare of mathematician is a sequence ##\varepsilon_n## that tends to infinity, as ##n \to 0##"
    Paul Halmos
     
  9. Jun 11, 2016 #8
    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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