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Where do mathematical inequalities come from?

  1. Oct 27, 2016 #1
    what do you think are the inspirations or motivations that lead to inequality statements like am-gm, bernoullie's inequality, etc...? are they inspired by physics, engineering...? learning them for the first time made me wonder where they came from. thanks!
     
  2. jcsd
  3. Oct 27, 2016 #2

    Simon Bridge

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    Inequality statements are inspired by the desire to communicate.
    Every time you want to say that something occupies all values up to (and maybe including) a certain one, you will need an inequality statement.
    Like, I am working all "days from now up to next thursday inclusive" is an inequality statement.
     
  4. Oct 28, 2016 #3

    symbolipoint

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    Simon Bridge's response makes so good sense that I want to apply TWO "like"s to it but doing so only cancels the first "like".
     
  5. Oct 28, 2016 #4

    Simon Bridge

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    Maths is a language ... :)
     
  6. Oct 28, 2016 #5

    Simon Bridge

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    For instance:
    If d is a day in which I am working, and today is day a, and "next Thursday" is day t, then I am working: ##a\leq d \leq t##
    If I start work tomorrow, instead, then ##a < d \leq t## ... it's a nice short way to write it down.
    If my days are numbered (and I don't count parts of days) then ##a < d \leq t## is the same as ##a+1 \leq d \leq t## because a+1 will be the day after today.
     
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