Question

What exactly do people mean by "small numbers"?

Answer 1

which people ? tell me? :O

Answer 2

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

Answer 3

A number is smaller if it is less than another number

Answer 4

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

Answer 5

It's all subjective.

Answer 6

-10000000000000000000000000000000 is an extremely large negative number.

Answer 7

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

Answer 8

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

Answer 9

$$\varepsilon$$

Answer 10

Good point, they even point out the epsilon.

Answer 11

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

Answer 12

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

Answer 13

^that readily extends to complex numbers :)

Answer 14

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 !

Answer 15

It also extends to arbitrary normed vector spaces

Answer 16

As skull already mentioned : It depends on the context.

Answer 17

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

Answer 18

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.

Answer 19

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

Answer 20

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

Answer 21

is an infinitesimal a small number?

Answer 22

im not even sure if an infinitesimal is a number

Answer 23

I would disagree with your sorting example. I would say that you are talking about sorting from least to greatest, not smallest to biggest.

Answer 24

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

Answer 25

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

Answer 26

So, @Alchemista if i asked for; the number which is smallest in magnitude , you would say that is tautology? [maybe you are right]

Answer 27

Correct.