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Do the Real Numbers Exist?

blog.kevmod.com

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Re: Do the Real Numbers Exist?

#21

Post by drdec »

sorokod wrote: post #12
drdec wrote: post #4

Earlier quoted context omitted.

I assume you mean in the physical sense? What if you get down to the quantum level? You don't have a straight line in the Euclidean sense any longer.

Do you question the existence of triangles and their mathematical properties?

Absolutely. There's no reason to believe space is Euclidean, in fact, relativity says it is curved. Quantum mechanics says that it is not infinitely divisible.

Re: Do the Real Numbers Exist?

#22

Post by drdec »

voxl wrote: post #7
drdec wrote: post #4

Earlier quoted context omitted.

I assume you mean in the physical sense? What if you get down to the quantum level? You don't have a straight line in the Euclidean sense any longer.

Yeah instead you have probability theory baked right in, real numbers and all!

You are conflating a mathematical model with reality, begging the question as it were.

Re: Do the Real Numbers Exist?

#23

Post by smadge »

threatofrain wrote: post #20
smadge wrote: post #5

Numbers aren’t real.

In casual terms, many number systems are "real enough" for people because they seem to form an adequate theory for modeling problems.

True but then the question should be “how well does this fake thing model this real thing?” Not “does this fake thing exist?”

Re: Do the Real Numbers Exist?

#26

Post by gsinclair »

sorokod wrote: post #12
drdec wrote: post #4

Earlier quoted context omitted.

I assume you mean in the physical sense? What if you get down to the quantum level? You don't have a straight line in the Euclidean sense any longer.

Do you question the existence of triangles and their mathematical properties?

It depends what you mean by “existence”. Mathematical triangles are ideal conceptions that exist only in our minds.

Re: Do the Real Numbers Exist?

#27

Post by zeebeecee »

Do integers exist? Do sequences of integers exist? If they do, so do the real numbers.

This is because any positive real number has a decimal expansion which determines it. For example pi = 3.1415926535... or 1/3 = 0.3333333...

Re: Do the Real Numbers Exist?

#28

Post by mbrodersen »

mensetmanusman wrote: post #25
mbrodersen wrote: post #24

Real numbers are abstractions. And abstractions are embedded in Physics. So if you believe that Physics is real then Real numbers are also real .

Abstractions are emergent properties of the laws of physics.

The “laws of physics” are mathematical models (abstractions) created by humans. And those abstractions are embedded in the physical world (our brains, written text, magnetic disks etc.)

Re: Do the Real Numbers Exist?

#29

Post by somat »

If I understand correctly, the problem is not so much real numbers, but real number that are not otherwise defined(integers, rational numbers, floating point numbers, etc) call them pure real numbers.

Because while it is easy to imagine there are numbers that are not defined, the minute you try define what they are... they are now defined, thus the problem/paradox, can something exist that is not defined?

Re: Do the Real Numbers Exist?

#30

Post by voxl »

drdec wrote: post #22
voxl wrote: post #7

Earlier quoted context omitted.

Yeah instead you have probability theory baked right in, real numbers and all!

You are conflating a mathematical model with reality, begging the question as it were.

Sure, otherwise you're just solipsistic, we have to assume things exist, it's how you make progress. If you think quantum is "the real stuff that exists" then you should assume, for now, that the model actually models something, and our best guess is that it's merely probability theory.
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