Uhhhh 1+1=2 that's enough math for me...
Uhhhh 1+1=2 that's enough math for me...
No it doesn't stupid, it equals a window.Originally Posted by Bert
Proof: 1 and 1 are the side parts of the window, + is the cross bit that goes in the middle, and = is the top and bottom parts of the window frame. Therefore 1 + 1 = a window
Damn HOOT you're too smart for me. Can you teach em the ways of your mathness?
I asked my friend to prove 2 > 1. He said 2 - 1 > 0 therefore 2 > 1
:D
However, this is actually an inherent flaw in the decimal system, because the concept of infinity is impossible. --Dragonflame
It's non-intuitive, but things still behave in a certain way even when you throw undefined values into things, like infinity. Infinity is undefined, in that it has no value; but introducing it into an equation doesn't blow the doors off the hinges and make everything else become completely random. Infinity still has "properties", I guess you can say. There are some branches of mathematics which reject the notion of infinity entirely, but it's not necessary to do so.
Mathematics in general is about concepts, not about real tangible things. You get to make up the rules when you form your own branch of mathematics. It just so happens that some branches fit with reality better. If you demand that a branch of math fit reality PERFECTLY, then you probably want physics, not pure mathematics. That's my take on it anyways.
But numbers must always be looked at in their simplest terms when using theory, so 9*(1/9)=1. The number 1 is not a ratio between two integers (in simplest terms), and therefore .999.... cannot be expressed as a ratio between two integers and is thusly an irrational number. --SeedRankLou
Huh?
To quote wikipedia:
Each rational number can be written in many forms, for example 3/6 = 2/4 = 1/2. The simplest form is when a and b have no common factors, and every rational number has a simplest form of this type. The decimal expansion of a rational number is either finite or eventually periodic, and this property characterises rational numbers. A real number that is not rational is called an irrational number.
1/9 is clearly rational, and .999... is clearly the (periodic) decimal expansion of 1/9. 1/1 is also clearly rational.
Won't that mean that every number is equal to every other number? --HOOTERS
Huh?
Sooner or later you have to run out of numbers to stick in between.
No. For example between 1 and 2, you have 1.1, 1.01, 1.001, 1.0001, etc. etc. That pattern alone produces infinitely many numbers, all of which are between 1 and 2.
Incorrect. Yes, 1/9 is rational, but the decimal expansion of 1/9 ends with 8/9, as 9/9=1 not .999.... And even if you were right, and .999....=9/9, that would equal 1, which is not (in simplest terms) a ratio between two integers. Yes 1/1 is rational, but 1/1 is not in simplest terms, and when comparing numbers in theory you must use simplest terms. Either way, .999.... is an irrational number.
Last edited by SeeDRankLou; 05-11-2004 at 05:03 AM.
I was really wrong with my last post. I don't know what I'm saying any longer. Enough math for me for one day.
: The integers are rational numbers. Don't get bogged down by 'simplest terms', they aren't really important. If it helps you can express 1/1 and 2/1 as the 'simplest terms' (a/b with a and b having no common factors) for 1 and 2, since 1 is not considered a common factor. Think of writing 1 as shorthand for writing 1/1, the denominator is always there you just don't write it.
Proud to be the Unofficial Secret Illegal Enforcer of Eyes on Final Fantasy!
When I grow up, I want to go toBovineTrump University! - Ralph Wiggum
now that is pure maths. :D
Yeah, simplest terms is a completely artificial concept to make math easier to understand. 1 = 1/1 = .999..., and all three are rational (because, of course, they are the same number).
1) In mathematical theory (which I believe is what were are dealing with), simplest terms are always important. You don't say 2A=2(pi)r^2. You don't say .77e=.77mc^2. You don't say a^2 + b^2 + 10=c^2 +10. You can, but you don't. Simplest terms are always used in mathematical theory.
2) You are askewing definition. 2 and 2/1 are interchangable. 2 is an integer, is that to say 2/1 is not also an integer, even though 2/1=2? 1/1 is a fraction, but since 1/1=1 it is also an integer. I'm fairly certain that the definition is specifying a ratio of two integers that is not also an integer itself, or the definition could also go: any real number that cannot be expressed as an integer (making fractions irrational number). Example, integer is defined as any real number with no fractional component. Is that to say 2u0/5 (two and zero fifths) is a compound fraction and not an integer? Even though you can see a fractional component, 0/5=0, thus there is no fractional component.
P.S.: I love math too. This thread is awesome. I had to think about my rebuttle for a rather long time because you guys did give some good evidence to support this notion.
Last edited by SeeDRankLou; 05-11-2004 at 09:37 AM.
Heh, you guys are nuts. This whole thread makes my head hurt.
"Sagashi tsuzukete kita yo
Namae sae shiranai keredo
Tada hitotsu no omoi wo
Anata ni dewatashi takute"
- Radical Dreamers, Chrono Cross
"Why do humans hate and hurt each other? Everyone lives under the same blue sky...
Will there ever be any relief from the pain of losing what was precious to us?
When will it be the day we can understand what all this loneliness and sorrow was for?
In short, we may be repeating the same mistake we made 500 years ago..."
- Man in Shevat, Xenogears
Okay, this proof's been buggin me since yesterday and I know why now.
For a proof to be a proof, there can be no counter example. In your proof 9/9 = 1 IS the counter example unless you can already prove to me that 0.9 = 1. If you don't ALREADY accept and have already proved that 0.9 = 1 this theory is no good.
You're in an endless loop, as you have to accept that 0.9 = 1 to prove that 0.9 = 1, which mean that you have to accept that 0.9 = 1 to prove that 0.9 = 1, etc...
BoB: Huh, good point, I don't know where I got the 8 from.
Anyway, now I'm really intrigued because, as proved before:
1/3 + 1/3 = 2/3 + 1/3 = 3/3 = 1
0.3 + 0.3 = 0.6 + 0.3 = 0.9 = 1
Okay, so this shows that we can add infinitely repeating numbers together.
But look at this:
2/3 + 2/3 + 2/3 = 6/3 = 2
but
0.6 + 0.6 + 0.6 = 0.18
So why the discrepancy?
I'm sure that this post has some mathematical flaws in it but it's fun to throw around some numbers and try to explain what's happening.
EDIT: Okay, this is a much better post.
Last edited by Flying Mullet; 05-11-2004 at 03:03 PM.
I think you mean:
0.6 + 0.6 + 0.6 = 1.8
and what gives there
The discrepancy is the inaccurateness of how you're adding the decimal representation of the fractions. You're only looking at what's visible and adding that, but not taking into account the carry-overs from the next decimal place which is implied by the bar, then the carry overs from the one after that and so on, hence why you appear to have such a big error.
What you're reading and adding is 0.6 + 0.6 + 0.6, which will give you 1.8. But since the true number you're adding is 0.6, each item you're adding is 0.06 away from what you should be adding, and these errors themselves add up to give a 0.2 error in your final answer. Then you're sticking the bar back in again, which yet again changes the answer you got, by adding 0.08. Which doesn't actually mean anything, it's only adding that particular value because that happens to be what's after the decimal point in that particular calculation. You can't just ignore the bar in your calculations then stick it back in at the end and hope it's fine, you need to take it into account all the way through
Maybe I do, and maybe I don't.I think you mean:
0.6 + 0.6 + 0.6 = 1.8
and what gives there
And yes, you are right. And this also shows two things:
Why 1.9 != 2
Why "1/3 + 1/3 + 1/3 = 1" and/or "0.3 + 0.3 + 0.3 = 1" are not accepted proofs for 0.9 = 1
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