If you have a ruler then in school, no matter how accurate it is, it can always be made more accurate, shortened to infinity perhaps, smaller than the distance between atoms, will it ever be completely accurate then? I understand math can be used to count e.g. 3 apples, but you also have PI which theoretically can have infinite decimals, you got the same problem there
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Is the subject math really logical?
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It can be that what you are talking about is exactly like Pi, and that until you get down to the absolute smallest measurement, is just an estimate until then, etc.
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Not until you can base all of your measurements on the absolute smallest measurement, which I don't know that we've found yet, etc.
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The Planck scale: relativity meets quantum mechanics meets gravity. (from Einstein Light)
The Planck scale: relativity meets quantum mechanics meets gravity. An explantion of Galilean relativity, electromagnetism and their apparent incompatibility; an explanation of Einstein's relativity resolves this problem, and some consequences of relativity. Planck units, Planck length, Planck...
www.phys.unsw.edu.au
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Well, what you're really trying to measure/get totally accurate is the space(s) between/in-between, and what truly counts as one true unit probably?
That's going to be exceedingly small probably, etc.
I don't think we've found it yet, etc.
God Bless.
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Yeah, I need more knowledge. And like, a lot more knowledge, etc. But knowledge that I am going to be working on getting more of here hopefully pretty soon, etc.
God Bless.
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Is it like when Indiana Jones stood in front of those glowing aliens and wanted unlimited knowlegde?
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Been a long time since I've seen that one?
Had to look it up to know which one you were referring to.
But I did mean knowledge the old fashioned way though, etc. Something I plan to take up more again hopefully here pretty soon, etc.
God Bless.
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PloverWing
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The subject line, "Is the subject math really logical?", seems to ask whether mathematics rests on a foundation of logic and proofs.
The original post, however, asks whether perfectly exact and precise measurement is possible in the physical world.
These are two different questions. Which one did you have in mind?
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I don't think you can shorten a ruler to infinity.
Once it hits the Planck length, that's all she wrote.
Yes.
On paper, yes.
Re the title of this thread:
If 100/100=1
And 10/10=1
And 1/1=1
What do 0/0 equal?
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PloverWing
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If I put my Theory of Computing hat on, I'll say that the division function is a partial function, not a total function, and it is undefined when the second argument is 0.
If I put my Calculus hat on, we can talk about limits. The limit of f(x)/g(x) as the numerator and denominator approach zero depends on what f and g are. You seem to be sketching out the limit of x/x as x approaches 0. The limit of this ratio is 1, as your sketch suggests. A different ratio might converge to a different value.
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Yeah, Morris Kline is one who hinted at this sort of thing years ago.
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I've read the OP a few times and... I think that their main point is that we can always make measurements more accurate... therefore everything we know is not correct because it could always be more accurate?
I don't know.
OP, a good thing to do in threads is that if you want to make a point, actually MAKE THE POINT. Don't just leave it half done like you have.
I don't know.
OP, a good thing to do in threads is that if you want to make a point, actually MAKE THE POINT. Don't just leave it half done like you have.
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You are are just plain ignorant.You all know I`m right but you ignore it to feel good
In your OP you mentioned PI having can "have infinite decimals" (translation infinite number of decimal places).
Using a proof by contradiction method mentioned in post #15, mathematicians using logic can prove this.
Warning this is an undergraduate pure mathematics problem requiring a number of pages and can cause migraine problems to the unwary.
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