Where are transfinite numbers located on the number line?
Where are transfinite numbers located on the number line?
Adam Myers
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Ryder Richardson
By definition, they're not on it
Adrian Taylor
If a number is not on the number line, how does one find out if it is bigger than any given number on the number line?
Jose Carter
>where are the numbers that aren't on the number line at on the number line
Christian Richardson
The number line only contains finite numbers
Brayden James
So, transfinite numbers aren't larger or smaller than finite numbers, they are just a different kind of number?
Josiah Diaz
Can someone give me a single practical application of ordinal/cardinal theory?
Blake Morgan
They are larger than any finite number
Kayden Kelly
Whenever you talk about sets, you usually want to talk about the number of elements they have.
William Murphy
So, if they were to be represented on a number line, they would be to the right of the finite numbers (positive, in this case)?
Easton Barnes
>say 1/0 is defined, what would the value be?
THERE IS NO WAY TO KNOW WHERE IT WOULD BE ON THE NUMBER LINE BECAUSE ITS NOT FUCKING ON IT
Benjamin Martin
Then in what way is it compared in magnitude to finite numbers?
Jace Hall
Besides knowing countable sets have Lebegue measure 0, there's nothing else.
Camden Flores
In one sense, you can think of transfinite numbers not as holding any particular location on the number line, but as being the entirety of the number line (or some infinite portion of it).
Adrian Foster
Depends on the norm. If you define a norm on [math]\mathbb{R} \cup \{\infty\}[/math] based on distance to the south pole in the projective real line, the distance between infinity and zero is 2, but for any real x, the distance is less.
Nathaniel Campbell
Where are complex numbers located on the real line?
Landon Price
Proof of consistency for Peano arithmetic
You can use an inaccessible cardinal for category theory
Camden Hall
Tyler Foster
The "real" component is on the number line at what ever it's value is. "4" means "4"
The "imaginary" component isn't on the number-line. We usually visualize a "number plane" with a 2nd axis at right-angles to the number line. "7i" is 7 units distant from the number line. So (4,7) is 4 steps to the "right" of (0,0) and 7 steps "up".
Noah Hernandez
>Proof of consistency for Peano arithmetic
literally Gödel's incompleteness theorems
Camden Cooper
dey exist in platonc space :)
Levi Hall
You have infinite real line, and behind it, after it "ends" there's another line for transfinite line, such that every element on that line is greater than anything on real line
Easton Anderson
I'm a brainlet, hence why I am asking the question in the OP. What's this mean in more basic bitch terms?
Juan Butler
What does the "ends" om quotes mean if the real line doesn't ever end?