Could the set of i numbers be in the null set? They dont have any true values, and the null set is the set of no values. So couldnt the null set include them?

{0} :rolleyes:

If you're asking "do complex numbers belong in the null set?" the answer is no.

- Warren

What do you mean by the "set of i numbers"?

Imaginary numbers? They most certainly do have "true values"!


The quick answer to your question is "No, the empty set does not include them (whatever you want to mean by "them"). The empty set does not include anything!"

The set of all "Pink Unicorns" IS the empty set because there are no pink unicorns (Quite a different situation from the set of all imaginary numbers!) but it is still wrong to say that "the empty set (OR the set of pink unicorns) includes pink unicorns. The empty set does not include anything.

To say that the empty set (or any set) includes something implies that that something exists.

This post is rated PG-13, and has not been approved for General Audiences. Kids shield your eyes.

empty set = {santa claus, tooth fairy, goldilocks, rumplestiltskin, etc.}

:bugeye: :m:

Emalius,
Great to see another mathematician here!
By i, I assume you mean "imaginary" numbers, the sqr rt of -1, whatever.
The answer to your question, I suppose, is what set you're looking at i.e. which set is Null a subset of?
If you are just looking at the reals then i doesn't exist, and so could be in Null.
However, i has been used in so many applications that, in general, it is hard to say that it doesn't exist. If you are familiar with fourier analysis, waveforms are broken down into sines and cosines using it. Einstein's equations use i to find distances in 4D space: sqr rt ( a^2 +b^2 +c^2 +{di}^2) where abc are lengths and d is a time measurement. This sqr rt is constant no matter who observes an object, although an observation of someone moving near light speed will disagree on a and d, for example, but the two disagreements will cancel each other out and the entire square root will be constant. This is a longworded way to say, give i a chance. If nothing else, it exists just to help us understand multiple dimensions and waveforms. And, anything that can be described can be put in a set, like flying pigs. There may not be any flying pigs, but they can be put in the set {things that do not exist} and so they aren't in the Null set either. So, yes I am contradicting what I said above, it doesn't matter what Null is a subset of, it is empty.
All that said, I really am glad to have another math person here. If you are so inclined, check out my "prime numbers" thread a page or two below the top, and please write something. I hope you stick around and challenge us with more ideas! :cool:

thanks for your help, although i probably shouldnt be reading this thread because my mommy says i can see PG movies :(

Originally posted by GundamWing
[B]This post is rated PG-13, and has not been approved for General Audiences. Kids shield your eyes.

empty set = {santa claus, tooth fairy, goldilocks, rumplestiltskin, etc.}


Actually, that set is not empty. The empty set is the set that contains no elements. Last I heard, existential import did not necessarily apply, so ficticious elements are indeed allowed.

Tom

The empty set doesn't include anything - even itself.

The set {} is the empty set.

The set {pink unicorns} is not empty.

The set {{}} is not empty, either.

I stand corrected. :)

Originally posted by GundamWing
I stand corrected. :)

You'd better hope that Santa forgives you else your socks will be full-o-rocks come 12/25

I said out loud " I like this James guy". Now I understand it better.