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