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ParthKohli

  • 2 years ago

What exactly do people mean by "small numbers"?

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  1. shubhamsrg
    • 2 years ago
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    which people ? tell me? :O

  2. skullpatrol
    • 2 years ago
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    As is true with all meaning it depends on the context.

  3. Eyad
    • 2 years ago
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    A number is smaller if it is less than another number

  4. ParthKohli
    • 2 years ago
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    I mean, sometimes they say that numbers like 1.0000001 are small, and sometimes they say that numbers like -10000000000000000000000000000000 are small.

  5. terenzreignz
    • 2 years ago
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    It's all subjective.

  6. skullpatrol
    • 2 years ago
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    -10000000000000000000000000000000 is an extremely large negative number.

  7. terenzreignz
    • 2 years ago
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    Why even worry, you're supposed to know from context?

  8. ParthKohli
    • 2 years ago
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    I conclude this post by noting down that it is all relative.

  9. Alchemista
    • 2 years ago
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    $$\varepsilon$$

  10. ParthKohli
    • 2 years ago
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    Good point, they even point out the epsilon.

  11. mathslover
    • 2 years ago
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    It depends Parth, 1 is smaller than 2 but greater than 0.

  12. Alchemista
    • 2 years ago
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    I would say \(a\) is smaller than \(b\) if \(|a| < |b|\)

  13. terenzreignz
    • 2 years ago
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    ^that readily extends to complex numbers :)

  14. mathslover
    • 2 years ago
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    We compare them . Like : 1.00000001 is smaller than 2 but is greater than 0 . We use the word "small" for some numbers comparing them to our real life examples. The speed of a car is 3 km/hr , we say it as small as the normal speed is 60-80 km/hr. And we say 3 cakes as enough for a person !

  15. Alchemista
    • 2 years ago
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    It also extends to arbitrary normed vector spaces

  16. mathslover
    • 2 years ago
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    As skull already mentioned : It depends on the context.

  17. skullpatrol
    • 2 years ago
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    When dealing with negative numbers it is better to think about "less than" rather than "smaller than."

  18. Alchemista
    • 2 years ago
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    There is actually a concept of a "small" number. It is what I stated above. It is in terms of "magnitude" for lack of a better word.

  19. UnkleRhaukus
    • 2 years ago
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    i think i agree with Eyad; smaller usually means less than for example i would say that: the smallest value that cosθ can be is negative one i dont agree that the smaller number is necessarily implying the smallest in magnitude

  20. UnkleRhaukus
    • 2 years ago
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    another example would be if we were asked to arrange the numbers from smallest to largest i would say that {-1000000000,0,1, 1.0000001,2,3,60,80} is correct and that {0,1, 1.0000001,2,3,60,80,-1000000000} is incorrect

  21. amistre64
    • 2 years ago
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    is an infinitesimal a small number?

  22. UnkleRhaukus
    • 2 years ago
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    im not even sure if an infinitesimal is a number

  23. Alchemista
    • 2 years ago
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    I would disagree with your sorting example. I would say that you are talking about sorting from least to greatest, not smallest to biggest.

  24. amistre64
    • 2 years ago
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    whatever it is, it is greater than zero but smaller than the smallest number

  25. Alchemista
    • 2 years ago
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    Less than, greater than != smaller than, bigger than

  26. UnkleRhaukus
    • 2 years ago
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    So, @Alchemista if i asked for; the number which is smallest in magnitude , you would say that is tautology? [maybe you are right]

  27. Alchemista
    • 2 years ago
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    Correct.

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