What exactly do people mean by "small numbers"?

- ParthKohli

What exactly do people mean by "small numbers"?

- schrodinger

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- shubhamsrg

which people ? tell me? :O

- skullpatrol

As is true with all meaning it depends on the context.

- anonymous

A number is smaller if it is less than another number

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## More answers

- ParthKohli

I mean, sometimes they say that numbers like 1.0000001 are small, and sometimes they say that numbers like -10000000000000000000000000000000 are small.

- terenzreignz

It's all subjective.

- skullpatrol

-10000000000000000000000000000000 is an extremely large negative number.

- terenzreignz

Why even worry, you're supposed to know from context?

- ParthKohli

I conclude this post by noting down that it is all relative.

- anonymous

$$\varepsilon$$

- ParthKohli

Good point, they even point out the epsilon.

- mathslover

It depends Parth, 1 is smaller than 2 but greater than 0.

- anonymous

I would say \(a\) is smaller than \(b\) if \(|a| < |b|\)

- terenzreignz

^that readily extends to complex numbers :)

- 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

It also extends to arbitrary normed vector spaces

- mathslover

As skull already mentioned : It depends on the context.

- skullpatrol

When dealing with negative numbers it is
better to think about "less than" rather than "smaller than."

- 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

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

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

is an infinitesimal a small number?

- UnkleRhaukus

im not even sure if an infinitesimal is a number

- 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

whatever it is, it is greater than zero but smaller than the smallest number

- anonymous

Less than, greater than != smaller than, bigger than

- 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

Correct.

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