A guy on research gate wrote:

A guy on research gate wrote:
>Rational Number Set is bigger than Natural Number Set!
...

He's an associate professor at a Department of Mathematics of a University.

researchgate.net/post/Rational_Number_Set_is_bigger_than_Natural_Number_SetIs_anything_wrong

Discuss:

bump

ofc it is to have rationals you need negatives and numerators and denominators (2 numbers for every number = combinations of integers)

are you trolling?

retard

>Chinese education

Anything in path that has to do with the concept of infinity, be it comparing different sizes of infinities or adding up an infinite series, is often going to give you stupid bullshit answers that are intuitively wrong even though they fit all your rules.

And why is that? Because the axiom of infinity is flawed and shouldn't be part of math.

>anything that goes against my personal intuition must be flawed/wrong
I see.

>the axiom of infinity is flawed and shouldn't be part of math

How is this wrong?
Every natural number is a rational number, but not every rational number is a natural number.

Well yea... The natural numbers can be put into the rational number set alongside all the infinite decimal iterations between natural numbers and imaginary numbers.

How the actual fuck do you brainlets think this is false?
OK, name a rational number that isn't natural. Easy, [math]\frac{1}{2}[/math], [math]\frac{3}{4}[/math], [math]\frac{355}{114}[/math], literally any negative number.
Now name a natural number that isn't rational. I'll wait.

There is a bijection from the Rationals to the Naturals, therefore they're the same size

infinity is in and of itself an intuition people have. If we relied purely on experience, we would only be able to work with numbers we can count to/construct

The rationals and naturals have the same cardinality ℵ

>cardinality is the only size which matters

top brainlet

>t. Dicklet

>he doesn't know the rational numbers and the natural numbers BOTH have measure zero
Brainlet confirmed.

>he doesn't realize measure theory is bullshit

Every natural number is not a rational number. After all, the natural numbers are finite ordinals while the rational numbers are equivalence classes of pairs of equivalence classes of pairs of finite ordinals. There is, however, a natural injection from the naturals into the rationals, so some people inaccurately say that natural numbers "are" rational numbers.

kill yourself fucking retard you don't know shit about how mathematics works

>mad because no actual argument
lmao

But that's a terrible way of comparing sets. For example:
Take the set of natural numbers, and add one to each element. Does it get smaller?

There's a way to pair every natural number with every rational

The natural numbers don't contain imaginary numbers, is that why the natural number set is smaller than the rational set?

>The guy from the researchgate post claims that Q and N are not of the same size because there is no bijection between them (cardinality definition of size)

>The defense given by and others is that cardinality is not the only definition of size, even though this discussion is not about size, it is specifically about cardinality

This really gets that high school invasion nogging jogging.

It is bigger, inclusion-wise

Depends on how you encode them in ZFC. In the standard encoding, N is not a subset of Q.

This board is super bad for a science and math board.