Question

What in the world is a normal number?

Answer 1

Stars*

Answer 2

@UnkleRhaukus @CliffSedge

Answer 3

are they the complement of non-normal numbers?

Answer 4

the opposite of abnormal numbers

Answer 5

Yes, @campbell_st, like we don't know if \(\rm \large \pi\) is a normal number or not.

I still don't know what a normal number is.

Answer 6

well normal numbers have an even distribution for the digits 0 to 9.... thats about the extent of my knowledge.

Answer 7

Yeah, as best as I can describe it, it is a number where all the digits in the number occur with equal frequency.

Answer 8

So 0.123456789987654321...... is a normal number?

Answer 9

not quite... you are a zero short.... I think

Answer 10

Yes, the zero counts.

Answer 11

And it assumes that the pattern repeats evenly

Answer 12

well I didn't know that

Answer 13

Yes... is this a normal number?

0.12345678998765432101234...

Answer 14

It might depend on the base and on where exactly the sequence of digits repeat.

Answer 15

So, can you give me an example of a normal number? I know about the Copeland-Erdos consant

Answer 16

Okay, so this one?
0.123456789101112131415617181920...

Answer 17

0.1234012340123401234...
is normal in base-5.

Answer 18

Oh, I'm talking about base 10.

Answer 19

In "0.123456789101112131415617181920..." the digit 1 appears to occur more frequently than the other digits. If we assume that it repeats the same pattern after the " . . . " then I would say, no, that is not normal in base-10.

Answer 20

what a strange concept

Answer 21

No, when it reaches ...2021222324, then 2 gets its share.

Answer 22

wow, this actually is a normal number.
http://en.wikipedia.org/wiki/Champernowne_constant

Answer 23

I remember looking it up when I was studying the normal distribution in statistics. I'm sure it has some practical applications, but not something I typically worry about.

Answer 24

i can not see how pi could be normal, there are not many zeros in decimal

Answer 25

@UnkleRhaukus It's indeterminate because we do not know all digits of pi.

Answer 26

π is assumed to be normal on empirical grounds, but empiricism does not constitute explanation....

Answer 27

Hmm, I wonder how a normal number can be normal.
For example, this is a normal number:
0.235711131719232931374143...

If you write it like this:
000000.235711131719232931374143...

then it becomes abnormal.

Answer 28

The normality depends on equal proportion of representation of digits, so you need a way to compute the proportion/probability of occurrence of digits in the number.
If it is a rational number, then you need to determine where the digits repeat/terminate.
For an irrational number, things get more tricky.

Answer 29

every number is normal , in base one

Answer 30

Okay, so is this a normal number?
0.123456789

Answer 31

Looks normal to me.
Each digit occurs with equal frequency.

Answer 32

But what if you write it as 0.123456789000000000000...? :D

Answer 33

Sig. figs. man, sig. figs.

Answer 34

but normality is a function of the notation used , not the value of the number

Answer 35

oh

Answer 36

i think it makes more sense to say a normal expression for a number ,

Answer 37

hmm okay. thanks