I just explained, very briefly, why I don't believe in free-will. You then critique my statements by saying you believe otherwise? Please sir, explain your belief.
.999... Equals exactly 1.
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I just explained, very briefly, why I don't believe in free-will. You then critique my statements by saying you believe otherwise? Please sir, explain your belief.
just curious
you are interested in the process of photon creation? :bugeye:
read this:
http://www.ingentaconnect.com/content/els/03759601/2000/00000274/00000005/art00542
But you aren't explaining why you believe. There IS a reason, tell me.
For example, many people believe in God. Why? Various reasons. Maybe they were brought up being told from day one that God exists. Or maybe one day they were perplexed when they asked themselves "where did all this come from?" Unable to supply a satisfactory explanation, they created a god in their own mind to deal with internal struggle. Another reason is that human, by nature, want to feel like they matter and they serve for some purpose other than themselves. For some people, this is being a devoted teacher. Some like working with sick children everyday. For a lot of people, it's being a part of God's "plan."
That's a brief explanation of why people believe in a god. Why do you believe free-will exists? Answers like "I just know" or "I can tell" are just restatements of the word "belief." Where is your logical path of reasoning?
'' "where did all this come from?" Unable to supply a satisfactory explanation, they created a god in their own mind to deal with internal struggle.''
... and then came relativity.
Relativity explains that nothing has a free-will. Everything that ever happens is somehow already written into space and time well before we consider it. Outside the realm of consciousness is found to be a spacetime arena which is infinite in character. It stretched from alpha to possible omega, and everything physical was all frozen in time. This means that it says that our entire histories are all alined out, frozen in time. Any choice we have, and action we do, say or hear, there are all actions in time that is acting as though it in all-time. This way, Einstein took it that everything was predetermined.
... and then came relativity.
Relativity explains that nothing has a free-will. Everything that ever happens is somehow already written into space and time well before we consider it. Outside the realm of consciousness is found to be a spacetime arena which is infinite in character. It stretched from alpha to possible omega, and everything physical was all frozen in time. This means that it says that our entire histories are all alined out, frozen in time. Any choice we have, and action we do, say or hear, there are all actions in time that is acting as though it in all-time. This way, Einstein took it that everything was predetermined.
'Logical reasoning' is often a catchphrase for justifying what has already been decided upon.
:wallbang:
That make absolutely no sense.
:wallbang:
You have absolutely no idea of the point of this article, do you? It does not prove that photons have a non-zero mass. There is no way to experimentally prove that a photon's rest mass is identically zero because every physical measurement has some error. What an experiment can do is establish an upper bound (or "limit" as used in the vernacular) of the photon's rest mass. This experiment does exactly that by establishing an incredibly small upper bound on the photon's rest mass. This experiment provides yet more confirmation that the rest mass of a photon is zero.
Boy, has this gone off topic.
Cardin, the "0.111..." in the original equation is the same as 1/9.
1/9 = 0.111...
so,
9/9 = 0.999...
Or if you like:
1/3 = 0.333...
so,
3/3 = 0.999...
So what's the difference between 0.999... inches and one inch?
What do you get if you subtract 0.999... from 1?
Now, draqon:
Cardin, the "0.111..." in the original equation is the same as 1/9.
1/9 = 0.111...
so,
9/9 = 0.999...
Or if you like:
1/3 = 0.333...
so,
3/3 = 0.999...
So what's the difference between 0.999... inches and one inch?
What do you get if you subtract 0.999... from 1?
Now, draqon:
Infinity doesn't gave a limit, but 0.999... does. It is precisely because there is no limit to the number of 9's after the decimal point that we can say that there is no difference betwen 0.999... and 1.draqon said:
True. But, I didn't just "decide" that I don't believe it exists then try to justify it. Rather, I looked for explanations then came to a conclusion.
That's the question that always gives 0.999...=1 deniers fits. If 0.999!=1, then according to both formal mathematics and simple intuitive logic there must be some number between them, some difference. They invariably don't have an answer for what that number might be.
Good thing too!
Well what you're doing here is comparing decimals and fractions, not the same thing..obviously.
.999 inches and one inch?
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They are exactly the same thing. 0.111... is exactly 1/9.Well what you're doing here is comparing decimals and fractions, not the same thing..obviously.
Try again. The difference between one inch and 0.9 inches is 0.1 inches. Between one inch and 0.99 inches, 0.01 inches. Between one inch and 0.999 inches, 0.001 inches.That one shifts one place to the right for each added nine. In the limit, that one simply disappears. There is no such number as 0.000....1. The difference between one inch and 0.999... inches is zero inches, exactly.
So if I asked you what $$0.5 - \frac{1}{2}$$ you not only couldn't give me an answer, you think it's not even a valid mathematical expression because "They are different things"?Well what you're doing here is comparing decimals and fractions, not the same thing..obviously.
That's like saying "Base 8 maths isn't really maths, because we all know there's 10 digits in mathematics!". No, it's a matter of convention. Fractions and decimals are different ways of expressing things. Though decimals are much nicer when you're not dealing with rationals (which are, pretty much by definition, the only things representable as fractions). Infact, some very clever mathematicians would argue that the Reals are the decimals.
That page and many others on Gowers' site should provide you with plenty to think about. He's very much like Bertrand Russell in his ability to explain things about mathematics, never mind the fact they are/were Cambridge maths professors in the same college.
Enmos
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