ParthKohli
  • ParthKohli
What exactly do people mean by "small numbers"?
Mathematics
schrodinger
  • schrodinger
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shubhamsrg
  • shubhamsrg
which people ? tell me? :O
skullpatrol
  • skullpatrol
As is true with all meaning it depends on the context.
anonymous
  • anonymous
A number is smaller if it is less than another number

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ParthKohli
  • ParthKohli
I mean, sometimes they say that numbers like 1.0000001 are small, and sometimes they say that numbers like -10000000000000000000000000000000 are small.
terenzreignz
  • terenzreignz
It's all subjective.
skullpatrol
  • skullpatrol
-10000000000000000000000000000000 is an extremely large negative number.
terenzreignz
  • terenzreignz
Why even worry, you're supposed to know from context?
ParthKohli
  • ParthKohli
I conclude this post by noting down that it is all relative.
anonymous
  • anonymous
$$\varepsilon$$
ParthKohli
  • ParthKohli
Good point, they even point out the epsilon.
mathslover
  • mathslover
It depends Parth, 1 is smaller than 2 but greater than 0.
anonymous
  • anonymous
I would say \(a\) is smaller than \(b\) if \(|a| < |b|\)
terenzreignz
  • terenzreignz
^that readily extends to complex numbers :)
mathslover
  • mathslover
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 !
anonymous
  • anonymous
It also extends to arbitrary normed vector spaces
mathslover
  • mathslover
As skull already mentioned : It depends on the context.
skullpatrol
  • skullpatrol
When dealing with negative numbers it is better to think about "less than" rather than "smaller than."
anonymous
  • anonymous
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.
UnkleRhaukus
  • UnkleRhaukus
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
UnkleRhaukus
  • UnkleRhaukus
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
amistre64
  • amistre64
is an infinitesimal a small number?
UnkleRhaukus
  • UnkleRhaukus
im not even sure if an infinitesimal is a number
anonymous
  • anonymous
I would disagree with your sorting example. I would say that you are talking about sorting from least to greatest, not smallest to biggest.
amistre64
  • amistre64
whatever it is, it is greater than zero but smaller than the smallest number
anonymous
  • anonymous
Less than, greater than != smaller than, bigger than
UnkleRhaukus
  • UnkleRhaukus
So, @Alchemista if i asked for; the number which is smallest in magnitude , you would say that is tautology? [maybe you are right]
anonymous
  • anonymous
Correct.

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