Looking at the title, I'd deduce that this thread is about different ways of representing the same value.
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Looking at the title, I'd deduce that this thread is about different ways of representing the same value.
But 1/3 can be represented as a decimal! .3 Repeating. And 1 is also a decimal. .9 Repeating. Whether it seems to make sense that a number that never quite reaches one is the same as one makes no difference, there are still countless proofs that say so and it is accepted by mathematicians as fact.
Again, you are constraining mathematics to time.Quote:
Originally Posted by spockman
I'd like to see these proofs of 1/3 equaling .3 repeating, I'll have a look around the web to see, or you can post them.Quote:
Originally Posted by spockman
EDIT: Alright I'm back, and every proof I've seen continoues to rely on the fact that 1/x equals an infinite string of .xxxx repeating.
I already did it for you.
Multiply .333~ by 10 and then minus .333~. This is 9 * .333~, and you should have got 3. If 9 * .333~ is 3 then .333~ must be 1/3.
And I also said try to long divide 3 into 1.0000000000...
If you're claiming that 1/3 cannot be represented as a decimal, that's logically equivalent to saying that, for example, 1/2 can't be represented either. Why?Quote:
Originally Posted by LucidDreamGod
Consider base 9. Now, 1/3 in base 9 is physically exactly the same as 1/3 in base 10, because 3<9. In other words, if you took a pie and cut it up into 3 pieces where 3 is in base 9, those pieces would be the exact same as they would be if 3 was in base 10.
Now, if you do the long division, you will see that, in base 9, 1/3 = 0.3
And in base 9, 1/2 = 0.4~
In other words, by your logic, 1/2 cannot be represented by a decimal since it has a repeating decimal representation in base 9.
I guess I didn't see .9 repeating in the same way you guys see it. I guess maybe by the human rules of mathimatics you guys are right, but when I see a .999 with infinite 9999s arcossed it I never see how it could be a 1. but if you want to bring rules like x10 makes the decimal go over a place to the right, if you want to look at .9999 repeating as a static number that can fit into equations other then fractions, then I guess your right.
I'm beginning to understand that .999 repeating is just a symbol of the number that isn't actually an infinite string of 9's but the only way to represent the number that is not supposed to be a process in an equation.
Lol, I guess you guys convinced me that this debate is a bit more complex then I thought :P.
Xei, thanks for actually giving a proof that didn't assume that .999 already equals 1.
So an amount of something infinately close to zero is nothing? I guess that makes a little bit of sense. Obviously it would have to be 0.00000 repeating, and since it is infinitely close it would never have a one in it...
Do things like that have a place in reality beyond mathematical inquiry though?
One could argue that negative numbers or imaginary numbers have no physical significance, yet there's no way the physical sciences could have been advanced to where they are today without them. Similarly, there's no way we could have the technology we do today without the foundation of real analysis.
I agree that .9 repeated equals 1 in mathematics and such, but the logic that .9 repeated is infinitely close to 1, but isn't 1 is sound.Quote:
Originally Posted by Black_Eagle
I am now going to leave this thread and never return. I will shut it out of my mind and hit myself whenever I see it or think about it... or hear about it.
This is a place of evil.
I'm constraining numerical mathematics to the constraints of calculus...Quote:
Again, you are constraining mathematics to time.
Math is based in logic, you ignoramus. 0.9~ LOGICALLY EQUALS 1.Quote:
Originally Posted by Black_Eagle
YES, AND I UNDERSTAND WHY .9~ EQUALS 1, JACKASS! I'M JUST TRYING TO SYMPATHIZE WITH PEOPLE WHO STILL BELIEVE .9~ DOES NOT EQUAL 1, BECAUSE THEIR LOGIC MAKES SENSE AND ISN'T NECESSARILY FLAWED, BUT IS INCORRECT ONLY BECAUSE OF THE RULES OF MATHEMATICS AND THE WAY THINGS ARE REPRESENTED!Quote:
Originally Posted by drewmandan
LOOK AT ME. I CAME BACK TO THIS THREAD AND AM NOW TALKING IN CAPS! LOOK WHAT IT'S DONE TO ME! THIS THREAD IS EEEEVVIIIIILLLLL!!!!
/thread
Yeah, how dare the rules of mathematics come into a discussion about mathematics. Yeah, we should all just go by gut feeling.Quote:
Originally Posted by Black_Eagle
GOBBLE GOBBLE GOBBLE!Quote:
Originally Posted by drewmandan
i
Their logic really doesn't make sense... what is the logical argument for .999~ not equalling 1?
lol, k guys, can we not just say that if you round off .9 repeated at any point it does not equal one, but if it does go on for infinity it is the same as 1? I think people who say it does not equal one are thinking of it if it get cuts off at some point still.
Yes, but let's be clear. It doesn't "go". It just "is". It's a static number, NOT a process.Quote:
Originally Posted by tkdyo
I say we turn this into sensless banter.
AHDHEHNCZ OMBIES
What does everyone here mean when they say .9 repeating is 1?
Do you mean it might as well be one, or that .9 repeating actually doesn't exist and only 1 exists?
I mean, you all mentioned 1/3.
. . . . . . 0.33333
1/3 = 3|1.0
Obviously 1/3 represents a finite value, .3 repeating represents 1/3 but is infinitely close to 1/3. .3 repeating means it is continuously trying to show what the decimal form of 1/3 is but can not. At least that is what it looks like from the perspective of being outside of a math community.
I think that simply by its nature any base will enter into a point where it can not accurately portray something as a finite value which another base could portray.
My problem is that since .9 repeating can't be accurately depicted as a finite number with the base it is using, I can't say that it is 1. I just can't say .9 repeating equals exactly one because I think .9 repeating represents one but doesn't equal one. If that even makes since.
I just don't see why saying making .3repeating infinite makes it suddenly a finite value of 1/3. There is no point, even if endless, where .333333333 equals exactly 1/3. I think it is a failure in the nature of numbers and number conversion.
So if it is a failure of number conversion, then .99999 repeating is exactly 1, only because of the nature of the conversion it can't be shown to be 1. Which means that the decimal value of .9999 does not equal 1 but represents a number using something other than the base unit it is using that is exactly 1.
Frankly, Sandform, you don't know what the hell you're talking about. 0.9~ = 1 in the same sense that 2/4 = 1/2. It's not "trying" to be 1. It's a static, unchanging number.Quote:
Originally Posted by Sandform
You at least have to admit that if you view it like it is supposed to be, it should never reach one, but it does somehow.
If by "supposed", you mean "incorrectly", then yes.Quote:
Originally Posted by LucidDreamGod
A common misconseption is that repeating numbers are not rational numbers. They are.
1 - 0.9999... = 0.000...1
Is that a number? An infinite number of 0's after a decimal and before 1?