countably infinite set
countably infinite set
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Give me a natural number and I give you its successor.
Give me a real number and I can not.
yes yes very funny OP
inb4 people respond seriously
All natural numbers are real numbers.
You can't because real numbers don't exist
Countably infinite just means that every element has an element "in front of" it
Rational numbers are countable
Now what, big boy?
he bounds mathematics with human limitations
don't you realize math is the language of GOD
how can something that is real also not be real?
Not true. There's simply a subset of the real numbers that go by the same names as natural numbers.
If two sets are both unique and identical then they're the same set
Identical sets are by definition unique, so yes. I guess he could've been more clear and said
Give me a natural number and I give you its successor
Give me a non-natural real number and I can not
But what he meant was clear from context, so this entire argument is dumb.
Is our perception real?
So in other words they're real numbers. Got it
You can basically count on both sides, either (n+1)/q or n/(q+1).
"Countable" is vague. You can count parts of an infinite set, but you can't complete the synthesis, that's what makes it infinite.
Finding a bijection between the elements of some set and the natural numbers is literally counting them so the terminology is instructive.
e.g. there is a row of shoes, we count them by successively assigning natural numbers to them.
A mathematics major would have some quip explaining how infinity is but at the end of the day, he will hust be one more retard in a sea of retards called mathlets who only vaguely pretend to understand definitions of infinity, meanwhile being unable to produce an example of infinity being used towards solution of any real world problem.
It's really not a maths concept at all. Mathlets assume otherwise.
Don't take math too seriously, it's mostly just bullshit.
the set of natural numbers includes ALL natural numbers
the last natural number is a number
the set of natural numbers does not contain the last natural number
There is no "last natural number", or "greatest natural number". This is why the set is said to be infinite, i.e. not finite.
Retard learn how to use Veeky Forums
He thinks (You)'s are upvotes
go back to your redit faggots
Countably infinite = graduated.
how can numbers be real if our eyes aren't real
meanwhile being unable to produce an example of infinity being used towards solution of any real world problem.
On the top of my head I can name dozens of examples where infinity and concepts developed with infinity are used in real world problems.
Do you honestly think that Engineering would work without "infinite sums".
Have you even taken *any* engineering class and seen where these mathematical concepts are used literally everywhere?
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