.999... Equals exactly 1.

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draqon said:
The mathematicians like everything absolute, like it is definite as a rock. The so called limit formula is the definition that implies that a limit to the .9999 to the infinite equals 1. This definition is self contradicting because INFINITY DOES NOT HAVE A LIMIT but they dismiss it because just as they say that photon does not have mass (which it does 10^-50g) they dismiss this as well because as they say it is NEGLIGIBLE. I really hate this but if you were asked what is the .9999 really equal to, understand that by human mathematics definition it is equal to 1, when in reality it does not.

Absane learned the definition, every book has it allright, every mathematician says it allright, well its all an assumption, its all based on an assumption that infinity does have a limit.

AND NO I DON'T PULL THIS STUFF OUT OF MY ASS: http://www.aip.org/pnu/2003/split/625-2.html
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Assigning mass to a photon is not logical, but you know that already.

Assigning a specific mass-energy to a photon is completely off-the-wall, but you know that already.

How could each and every photon have an energy equivalent to exactly 10^-53 kg, when E = hv, and v is variable (ex: 'blue' photons have a different v than 'red' photons)? The number you are quoting is a theoretical upper limit, and so, should obviously not be applied in the way that you imply.

Am I misinterpreting what you're saying, or were you just making fun the banality of the entire .999 ~ 1 "debate"?
 
shalayka said:
How could each and every photon have an energy equivalent to exactly 10^-53 kg
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its not, its a limit...I am a believer in string theory, the mass of photons is different from my point of view because strings of energy are never in the same location for any particle at any time.

The mass of the photon which is predicted by string theory depends on the energy of the string mode which represents the photon. This energy includes a contribution from the Casimir effect, namely from quantum fluctuations in the string.
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Do you have anything I can read on this? Not even sure what I would search for..it's kinda interesting.

haha, take it easy..I was accusing myself of hijacking.
 
Well I meant more of what you meant when you said

nothing changed, what happened is that the photons were absorbed into atoms of the glass and the energy waves transfered from atom to atom to knock out a new photon particle from a new glass atom on the other side of the glass cup.
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"they say that photon does not have mass (which it does 10^-50g)"

Then why make statements like this?

That's kind of funny how I said it's an upper limit, then you truncate my quote and repeat what I said, making it sound like I was the one who was confused. Whatever.

The point of an upper limit is that there is still a chance that it's actually 0. So don't go interpreting it as a fact, when it's certainly anything but. Perhaps an analogy will help: The theoretical upper limit of my opinion of your scientific integrity is "superb", but in actuality, it's nowhere close to that. Quit dancing around and post some real information about this "string theory" thing that you're referring to, otherwise you're just using a prop. I enjoy general relativity (and string theory) too much to have it used in such a way.
 
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Absane said:
Ok? Also, BY DEFINITION, $$\lim_{n \rightarrow \infty} \sum_{i=1}^{n} \frac{1}{10^i}$$ is equal to the limit of the sequence of partial sums $$(s_1, s_2, ... )$$ where $$s_n = \sum_{i=1}^{n} \frac{1}{10^i}$$. Does EVERYONE see this? We are NOT summing infinite terms by this definition... people seem to think that because summing an infinite number of terms is physically impossible we cannot describe what such a sum may look like.

OK, we notice two things people. The first... $$s_n = \sum_{i=1}^{n} \frac{1}{10^i}$$ is an non-decreasing. .
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Maybe I am missing something shouldn't those be summations of $$\frac{9}{10^i}$$
 
shalayka said:
The point of an upper limit is that there is still a chance that it's actually 0. So don't go interpreting it as a fact, when it's certainly anything but. Perhaps an analogy will help: The theoretical upper limit of my opinion of your scientific integrity is "superb", but in actuality, it's nowhere close to that.
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Well allright than...I interpret it as a fact or the assumption by me that it is not a 0 because the upper limit of 10^-53g exists and mathematicians interpret it as 0 as a fact which it is not because upper limit of 10^-53g is only an upper limit so it can be in between that and the 0.

So its all just assumptions.
 
draqon said:
Well allright than...I interpret it as a fact or the assumption by me that it is not a 0 because the upper limit of 10^-53g exists and mathematicians interpret it as 0 as a fact which it is not because upper limit of 10^-53g is only an upper limit so it can be in between that and the 0.

So its all just assumptions.
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No mathematician in their right mind would equate 0 to the unweighted range of 0 through 10^-53 inclusive.
 
shalayka said:
No mathematician in their right mind would equate 0 to the unweighted range of 0 through 10^-53 inclusive.
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physics and mathematics are different thing. Physics is reality. Do you agree or do you not agree to what is being stated in the prestigious highly notable physics journal I have quoted?
 
draqon said:
The mathematicians like everything absolute, like it is definite as a rock. The so called limit formula is the definition that implies that a limit to the .9999 to the infinite equals 1. This definition is self contradicting because INFINITY DOES NOT HAVE A LIMIT but they dismiss it because just as they say that photon does not have mass
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It makes more sense to say that the infinity must have an equavalent measureable set to constitute the limit of infinity. E.g. aleph_0 + aleph_0 = aleph_0. This would explain the expansion and contraction behavior of the universe. Conspansion would explain the evolution of a universe of any size (finite) or sizelessness (infinite). The evolution of lifeforms is evolving along with the universe. Nature itself is evolving in its own selectiveness.
 
draqon said:
The mathematicians like everything absolute, like it is definite as a rock. The so called limit formula is the definition that implies that a limit to the .9999 to the infinite equals 1. This definition is self contradicting because INFINITY DOES NOT HAVE A LIMIT but they dismiss it because just as they say that photon does not have mass (which it does 10^-50g) they dismiss this as well because as they say it is NEGLIGIBLE. I really hate this but if you were asked what is the .9999 really equal to, understand that by human mathematics definition it is equal to 1, when in reality it does not.
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In reality numbers have no physical properties. So, how is it you can talk about how 1 relates to other numbers?

And why does everyone refute the 0.999... = 1 claim by bringing photons into the discussion?

MY CLAIM... The rules of mathematics are a SUPERSET of the rules that reality go by.

Proof: Pick any rule of reality. It can be described mathematically. QED.

Absane learned the definition, every book has it allright, every mathematician says it allright, well its all an assumption, its all based on an assumption that infinity does have a limit.
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Huh? Infinity isn't a function for which a limit can be investigated.


AND NO I DON'T PULL THIS STUFF OUT OF MY ASS: http://www.aip.org/pnu/2003/split/625-2.html
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This paper fails to address mathematical axioms.
 
mapsdnasggeyerg said:
Maybe I am missing something shouldn't those be summations of $$\frac{9}{10^i}$$
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The OP said something about 0.111... so the whole point of my post was to address, in lazy mathematical laymen's terms, what 0.111... means and how we write it in strict mathematical notation.
 
draqon said:
You claim anything can be expressed in mathematics. Well express my consciousness of self.
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I said anything in reality can. Metaphysical stuff isn't what I would call "reality." Things like physics and the like predict the rules of how the physical universe operate. Describing free-will with mathematics is a bit contradictory, isn't it?

But then this is why I don't believe free-will exists... an unannounced willed action would cause an unpredictable reaction. In the long run, this would create large-scale chaos on the macro level (butterfly effect). In billions of years of existence, I think it's safe to say that only microlevel chaos exists... but even there, I'm not so sure it is chaos.
 
Absane said:
I said anything in reality can. Metaphysical stuff isn't what I would call "reality." Things like physics and the like predict the rules of how the physical universe operate. Describing free-will with mathematics is a bit contradictory, isn't it?

But then this is why I don't believe free-will exists... an unannounced willed action would cause an unpredictable reaction. In the long run, this would create large-scale chaos on the macro level (butterfly effect). In billions of years of existence, I think it's safe to say that only microlevel chaos exists... but even there, I'm not so sure it is chaos.
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well there you go all an assumption by you and me. I believe in free will and you do not. Meanwhile here we are talking to each other, being ourselves...which is undefined.
 
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