wtf wrote:Serendipper wrote:Or can you prove there are infinitely many real numbers?

I already did, three different ways: The tan/arctan bijection, the 1/x bijection, and Cantor's beautiful bijection between the reals and the irrationals. How many more proofs do you need?

I need one proof. You haven't proved

"The tan/arctan bijection, the 1/x bijection, and Cantor's beautiful bijection between the reals and the irrationals" until you prove there are infinite x.

First prove that, then you can prove the others.

Serendipper wrote:f it's bounded at 0 and 1, then it's not infinite. Show me how it's infinite if it's bounded.

It's infinite and it's bounded. It's an infinite set, and none of its elements are less than 0 or more than 1. Did you take high school math? Are you sitting here claiming the real numbers are finite? What's the largest one?

You didn't show anything, but simply called me stupid.

x = 1,2,3,4,5

2x = 2,4

The subset 2x cannot be bijected with x BECAUSE the set x is finite, but what does finite mean? (limited/bounded)

x = 1,2,3,4,5,...

2x = 2,4,6,8,10,...

The subset 2x can be bijected with itself BECAUSE the set x is infinite, but what does infinite mean? (unlimited/unbounded)

What do the three dots (...) mean? <-- you must define that BEFORE conveying what you mean by "bijection with a subset of itself".

The three dots mean "unbounded".

It is only after I understand that the three dots mean the set is unbounded that I can then proceed to understand what you mean by being bijected with a subset of itself, so the bijection cannot be the definition of the three dots.

It doesn't mater what set we choose:

Here's your (0,1) which is f(x) = 1/x where x>=1, so x = 1,2,3,4,5,....

f(x) = 1/1,1/2,1/3,1/4,1/5,....

You still have to show what the three dots mean before showing anything else.

Therefore, whatever you show as a result of understanding what the three dots mean then cannot be used to define what the three dots mean.

Your definition of the infinite is invalid due to circular reference.

IOW, if someone never encountered the concept of the infinite, they could not possibly understand the concept via that definition because already having an understanding of the infinite is required in order to understand the definition.Serendipper wrote:And you're appealing to the ridiculous.

Someone claiming there are only finitely many real numbers (or that the unit interval is unbounded) surely has the burden of proof.

You said before there can't be infinite oranges and you specifically said

"What on earth do you mean by conceptualizing infinitely many oranges? What are they made of?"But yet you can conceptualize infinite numbers lol

Well, to quote you again, "what are they made of?" Nothing? So then with "nothing" as your basis, you claim infinity exists in some way? Well they aren't nothing; they are concepts and your mind is finite.

Infinity cannot be conceptualized; we can work with the implications/ramifications of it, but we cannot conceptualize infinite real numbers.

Further, any universe in which anything can exist (and that includes all universes in imagination) there cannot also exist infinities because something cannot be conceived/beheld/perceived as a universe in imagination or reality without being bounded/finite/definite. The infinite makes existence impossible.

Peace, brother. All the best.

You're brother to someone who doesn't understand high school math?