Yes, here's my proof!
No, here's my proof!
Omg, I pressed the back button and deleted all my post.
In summary, infinity is a concept, you can't do arithmetic with infinity using +-x/. So it makes no sense 1/infinity. Nor do I get how you came to that conclusion based on 0.999~=1.
0.9999~x10=9.9999~, not 9.9999...0 (1/3x10=10/3=3+1/3, the 1/3 you multiplied is the same as the 1/3 you get at the end if you minus 3, ditto with 0.999~). Nor does 0.000...1 = 0, nor is it an infinite series, so the following arguements aren't valid.
If you repeat the step infinitely, then it is the same as reaching the line or filling the glass.
Not sure what K2Grey mean by fixed value. What I assume you mean is 0.9 repeating does not equate to the infinite series with sum of 9/10^n?
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I think explaining the concept behind this equality is useless. You either believe in all the concepts of higher level math, or you don't.
I will say that higher level math is the basis for just about every modern technology in existence. You can deny the concept behind them all you want. But scientists and mathmaticians have used these "BS" concepts for ages on practical things that are tangible and do work.
Want an example? How about the computer you're reading this post on?
I reassert that the problem is in notation. As I am sure the members of an Asian Entertainment forum who are all posting in English can understand, meaning can be lost in translation.
The basis of my objection is that numbers are instructions. Each of those 9s means something—that you have closed the gap before the all the digits to the left of its place and 1 by exactly 9/10. It doesn’t matter how many of them there are – each 9 by definition falls short of reaching one. If your instructions are always to stop 10% short of finishing filling the glass then repeat ad infinitum how can you fill the glass without ignoring the instructions? If you think the glass is full tell that to the poor sap with the pipette who is stuck adding tiny drops to it for eternity. Just because I can’t define how short of the top of the glass you have come does not mean that you have filled it.
I believe K2grey meant that .999~=9/9 in response to my objections to filling the cup and walking down the number line. K2Grey’s objection I believe is the action of filling the cup and walking down the line indicates changes in value while .999~ is a value that will never change while my narrative sounded like I was describing a function instead. I agree that it is a fixed value. The walking and filling are merely illustrations of how we come to the value.
The problem is the decimal system because there is no way of truly representing 1/9, 1/3 or any other value that is not easily divisible except for a clumsy shorthand that had to be invented as an afterthought.
I believe that 1/3*3=1. I never questioned that. I will even accept your other assorted proofs that.999~=1. My confusion was created by the earlier proof in post 39 that appears to have been thrown out for procedural reasons in post 51 because it defines a concept rather than a number and therefore cannot be used with mathematical operators. I think this is what was causing Skylee’s confusion as well
Fractional notation is accurate. It means what it says. We should learn to use fractions again.
I am not saying the concepts are BS. I just want to understand.
Missouri.slim
Last edited by missouri.slim; 04-30-09 at 09:11 AM. Reason: I blinked when you took the picture
It seems the examples here should be more than convincing enough. But if you're still skeptical...
Have you at least learned Pre-Cal in school? Or at least a good grasp of high school Algebra/Geometry? If so, to understand simply read a Calculus book. No need to do problems. And no need to go in depth. But just reading and understanding the first few chapters will allow you to free your mind from the "restrictions" you've boxed yourself with.
Hey Meh, just wondering why would you want to call those concepts "BS" in the first place? If what I'm thinking is actually what you meant. Unless BS has another kind of meaning. i mean, from what you wrote, you obviously respect those concepts, right? Just don't write anything that could let anyone misunderstand you.
Actually, reading Missouri.slim's post, i think he did learn Pre-Cal. Reading everyone's posts here, I think it's safe to say everyone in this thread learned some basic Caculus, or we wouldn't be attracted to this thread, agree? We're here coz we love to discuss Maths. And from what I gather, most people here also love Physics?
I agree with you that explaining the concept behind this equality is useless. This just makes for something to tick your mind on when you have too much time or grey brain cells. It's not practical, just something that you might want to play with.
Is there any practicality in memorizing all the decimals of pi, except to flaunt your memory? Someone did that anyway. This thread is here because we want something interesting to discuss after work, looking for something to destress.
Don't take this TOO seriously guys, unless you're a mathematician and proving or disproving it could get you the Nobel prize.
skylee, is that a typo you made there? don't you mean
if .99999~ = 1, that would mean that 1/infinity = 1
coz 1/1 = 1
isn't that what you mean?
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Hey guys, actually pondering more...... it is never quite possible to divide exactly a cake into 3 parts. We only imagine the divided cake to be equal. But right down to the last molecule, there must be a part of a cake that is bigger or smaller than the other parts. Isn't that right?
Yes, 1/INF = 0.
If you want to be more precise, the limit of n to INF for 1/n = 0.
Yes it is a fixed value. Because 0.999... = 1
If you want to argue, consider this : If 0.999 is fixed at some value other than one, then where?
If we could, what are you gonna set as the x-axis and y-axis, dude?
I think you're wasting your time. Sorry.
That would also mean that 1 = INF. Wow good to know.
First, 0.000...1 = 0, if it exists.
So 0.999... - 0.000...1 = 0.999... = 1
And 0.999...0 is out of the question because the 1st condition of this topic is
0.999... with recurring 9's all the way...
Also, the math stated in post #39 is sound. See post #65 for an explanation of infinity and infinitesimal.
I don't think you will win me over by questioning my education. I was unaware I needed to post my curriculum vitae to join in on the thread. I will keep it in mind next time.
Like I said, I am not a mathemetician, and I assume you are. I did not say you were wrong-- I actually agreed that .9~=1. We agree on the what, we just have trouble with the why. I merely asked if each of your infinite places to the right of the decimal brings you 90% closer by definition of the number nine you will always fall 10% short of reaching one, just like Sysiphus never got that rock to the top of the hill. Even if there are infinite nines to the right as I know there are, they are still nines each closing the gap by 90%. I am merely trying to find help reconciling two things I know to be true but seem in conflict with one another. And yes, I realize that is a whole lotta nines.
I guess a calc book and a fifth of scotch is what I need. And a fifth of scotch=25.6 oz=25.5999~oz=.2 gallons=.1999~ gallons. See, I have been paying attention. I get it, every bottle with a terminating decimal has a twin with trailing 9's.
Missouri.Slim
Last edited by missouri.slim; 05-04-09 at 06:48 PM. Reason: clarification of fuzzy language
I think that Wolfram Mathworld has already been introduced as an authority in this thread. They (at least to my feeble non mathematical mind) seem to have a different definition of inifinitesimal:
An infinitesimal is some quantity that is explicitly nonzero and yet smaller in absolute value than any real quantity.
To me that reads as less than anything (smaller in absolute value than any real quantity) but more than nothing (explicitly nonzero).
Kind of like back in June of 1997 when Evander Holyfield's ear was infinitely close to Mike Tyson's mouth and yet Evander Holyfield's ear was not Mike Tyson's mouth.
I will go find a calculus book as Meh suggests and start working on a hangover and stop bothering you for now.
It has been fun,
Missouri.slim