Well, the exercise you botched has nothing to do with Einstein. Your hatred of Einstein seems to impede even your ability of learning simple math.
It will never happen, live with it, you just got pulled over by the police, they are taking you back.
1=0.999... infinities and box of chocolates..Phliosophy of Math...
- Thread starter Quantum Quack
- Start date
Well, the exercise you botched has nothing to do with Einstein. Your hatred of Einstein seems to impede even your ability of learning simple math.
It will never happen, live with it, you just got pulled over by the police, they are taking you back.
Yazata
Valued Senior Member
What does 0.(9) mean? Does it refer to a decimal point followed by an infinite series of 9's?
You just seem to be announcing that the value of the series and its limit are to be identified with one another. You may or may not be correct, but the question was and still is why.
If a decimal point followed by some finite number n of 9's is never one, and if adding yet another 9 to the series so that there's (n+1) 9's won't suddenly make it equal one either, then why shouldn't we conclude by mathematical induction that no series of 9's following a decimal point will ever equal one? If there's something wrong with that reasoning, what is it. (That's not rhetorical, I suspect that there is something wrong, and I want somebody to tell me, in a friendly fashion, at a level that I can understand, what it is.)
I've never said anything about calculus, beyond noting why Newton and Leibniz were willing to drop the infinitesimals from their calculations.
When I took calculus, we never went into this stuff in any depth. I'd guess that it's something that math majors are more likely to encounter in their analysis classes. I was never a math major.
But the thing is, if you, BillyT and Rpenner really think that you understand this stuff better than the rest of us laymen, then you have a choice to make. You can choose to insult us, put us down and belittle us because we intruded onto your turf and dared to try to think about things you think you know better. Or you guys can suck it up and try to do something that you've been totally incapable of doing so far -- teaching.
Seriously, one reason why a growing percentage of the general public is uninterested in and even hostile towards math and science is bacause math and science teaching is so often terrible. If math and science are presented in boot-camp style classes designed to wash as many students out as possible, when exercises are deadly drudgery and teaching is little more than rote memorization of material that must be taken on faith, it's no wonder that most students just say 'fuck this!' and turn their attention elsewhere.
Sciforums has the opportunity to be something more, to be better than that. It can actually make science and math interesting and help beginners get their minds around its concepts in interesting ways. That's not going to work when beginners who dare to show interest are met with insults, put-downs and snideness.
Make up your mind, Tach. If you want to insult me, I'll keep my "misconceptions" and I'll also think that you are an asshole. Maybe, if you guys are lucky, you'll permanently sour me on math and science too.
The alternative is to be helpful towards those of us who you're so sure don't understand. If you don't quite see how to respond to our points, and if that frustrates you, then perhaps you have some learning to do too.
One of the first things that teachers learn is that they don't really understand the material themselves, until they can lay it out and make it comprehensible to people who are unfamiliar with it. If they respond by putting down their students because they don't already know all of it, they will never succeed in teaching.
You do understand how long division works, though? It's a method you learn at a fairly early stage.Yazata said:
The reference is that long division is done in steps, or parts. To divide, say, 469 by 7, you say 7 divides 46 6 times with remainder 4, (actually 40), then 7 divides 49 7 times with remainder 0, there are no more digits so we're done in two "steps", and the "result" is 67.
Note that "steps" and "results" have nothing to do with the fact that mathematically, 469/7 = 67.
This is the method, or algorithm, most people associate with "long" division.
Ok, but the infinite number of places in a repeating decimal like 0.999... isn''t "responsible", it doesn't "cause" anything.
Can you envisage a process that doesn't continue but happens "immediately"? That's the concept I was trying to explain: long division as the usual step by step process, or as a parallel process, since mathematics isn't concerned about how numbers are divided (you can use any method you like).
Motor Daddy
Valued Senior Member
Tach, Face it, when you divide 1 whole into:
2 pieces the pieces are 50% of what they used to be, but there are 2 of them.
4 pieces the pieces are 25% of what they used to be, but there are 4 of them.
8 pieces the pieces are 12.5% of what they used to be, but there are 8 of them.
16 pieces the pieces are 6.25% of what they used to be, but there are 16 of them.
32 pieces the pieces are 3.125% of what they used to be, but there are 32 of them.
64 pieces the pieces are 1.5625% of what they used to be, but there are 64 of them.
128 pieces the pieces are 0.78125% of what they used to be, but there are 128 of them.
256 pieces the pieces are 0.390625% of what they used to be, but there are 256 of them.
512 pieces the pieces are 0.1953125% of what they used to be, but there are 512 of them.
1024 pieces the pieces are 0.09765625% of what they used to be, but there are 1024 of them.
2048 pieces the pieces are 0.048828125% of what they used to be, but there are 2048 of them.
4096 pieces the pieces are 0.0244140625% of what they used to be, but there are 4096 of them.
8193 pieces the pieces are 0.01220703125% of what they used to be, but there are 8193 of them.
16384 pieces the pieces are 0.006103515625% of what they used to be, but there are 16384 of them.
32768 pieces the pieces are 0.0030517578125% of what they used to be, but there are 32768 of them.
65536 pieces the pieces are 0.00152587890625% of what they used to be, but there are 65536 of them.
So the real question is, Tach, what percent of a whole are the pieces when there are an infinite number of them? Zero you say? You claim they are zero percent? I say BS!
2 pieces the pieces are 50% of what they used to be, but there are 2 of them.
4 pieces the pieces are 25% of what they used to be, but there are 4 of them.
8 pieces the pieces are 12.5% of what they used to be, but there are 8 of them.
16 pieces the pieces are 6.25% of what they used to be, but there are 16 of them.
32 pieces the pieces are 3.125% of what they used to be, but there are 32 of them.
64 pieces the pieces are 1.5625% of what they used to be, but there are 64 of them.
128 pieces the pieces are 0.78125% of what they used to be, but there are 128 of them.
256 pieces the pieces are 0.390625% of what they used to be, but there are 256 of them.
512 pieces the pieces are 0.1953125% of what they used to be, but there are 512 of them.
1024 pieces the pieces are 0.09765625% of what they used to be, but there are 1024 of them.
2048 pieces the pieces are 0.048828125% of what they used to be, but there are 2048 of them.
4096 pieces the pieces are 0.0244140625% of what they used to be, but there are 4096 of them.
8193 pieces the pieces are 0.01220703125% of what they used to be, but there are 8193 of them.
16384 pieces the pieces are 0.006103515625% of what they used to be, but there are 16384 of them.
32768 pieces the pieces are 0.0030517578125% of what they used to be, but there are 32768 of them.
65536 pieces the pieces are 0.00152587890625% of what they used to be, but there are 65536 of them.
So the real question is, Tach, what percent of a whole are the pieces when there are an infinite number of them? Zero you say? You claim they are zero percent? I say BS!
Yep, that's the textbook definition.
I am not "announcing", this is the textbook definition.
Because this is how the concepts were constructed. And, yes, it is correct, there are no two ways about it.
Because there is an INFINITE number of 9's.
The number of 9's being added is infinite, you are thinking in finite terms.
Did you learn series? This is not a "math major" subject, it is an introductory subject.
None of us insulted you but you are clearly insulting us. Teaching is a two way street, we can try to teach you but you need to be willing and capable of learning.
I very much doubt it, it has a lot to do with the willingness and ability to learn. See above.
Today, you learned integer division. At this pace, over the next 30 years, you may learn division of real numbers.
Motor Daddy
Valued Senior Member
...but today was another day of ignorance for you. At this pace you will never understand it. I already told you the problem with your .999...=1, and that is that the remainder is not included in the percentage of .999..., so it can never equal 1.0. You are missing a piece, and it's called the remainder, and it never goes away, and you never include it in the total so your total will never be 100%!
Never!
Motor Daddy
Valued Senior Member
...and everybody else but you is driving the wrong sense on the freeway
According to Einstein I am correct! Are you trying to say that Einstein was wrong, that there really is an absolute truth?
Einstein never claimed that truth is relative, give it a rest.
I would not claim to "understand better" but to claim to me more logical than some posting here. I.e. I admit some things must be assumed and then one sees what flows from them by logic. That is what math is - an axiomatic based tautology.
I think my general method for finding the fraction equal to any Repeating Decimal, exposed in post 301 ,is both some "teaching" and helpful derivation from the axiom noramaly assumed and an understanding of the common base ten notational system. Together they allow a proof to follow logically that 1 = 0.999... Furthermore, my proof has appeal to those who don't want to (or can't) accept proofs using the limiting process.
Those who claim that 0.9999... is not 1.0 or true are (1) illogical, or (3) have assumed different axioms than common ones or (3) poorly understand the common base-10 notational system. (or several of these) or are (4) just internet trolls.
I agree that even at some of the better universities, there are some teachers significantly better than others, but none who your typical "beginning student" can not learn from. I have taught modern physics at Johns Hopkins and proctored labs when there as a graduate student. At Cornell, I was paid, privately, to tutor some people, even as an undergraduate. It may be egotistical, but I think in areas I know well, I am a better than average teacher. In many posts here, I have noted that I welcome the opportunity to respond to physics errors, even when the poster has shown near zero ability to learn, as that gives me the opportunity to teach to other readers who can, with out seeming to be pedantic or egotistical.
On more than one occasion I have been thanked for clarifying some points. Once at the end of the thank-you there was: "clink, clink, clink..." with a footnote telling that was the sound of his coins dropping. If I have insulted you (or anyone) I sincerely apologize. I don't think I have. I am sort a gentleman of the old school - don't do that except in rare, very well earned cases and don't use bad language either.
-------------
BTW I am deeply concerned by the drift of the better students away from the hard sciences and math. About 10 years ago I wrote a physic book in disguise, hopping to help some with this problem of national import. I knew my "target readers" would never knowingly open a physics book. Dark visitor tells of a possible comic disaster that could soon happen to Earth, making life impossible in the Northern Hemisphere by a sever new and permanent ice age there.* Trying to scare good students planning to get rich in wall street, some law firm, etc. with no current interest in physic to at least look to see if the disaster is possible. So Dark Visitor is written as if the approach of the small back hole, which slightly will change earth's orbit, is the report of a rich Southern Hemisphere astronomer, who has been studding Pluto's orbit with high precision. It is a matter of fact now, due to the location of Pluto in its highly inclined orbit plain that currently such high precision measurements of Pluto are only possible in the larger Southern latitudes. (Why only he knows the small black hole is approaching.) Getting Pluto's orbital parameters better defined is of too low interest to get any time on a space telescope and they are changed by further out asteroids too, so it ain't easy to see the BH's currently small but growing perturbation with months of careful measurements required.
*Even in the Southern Hemisphere many will die. With in a decades so much frozen water will be stored on land that no ports will still be operational. Washington DC will be under ~1oo feet of ICE by the end of the first decade. The first month ABH, After Black Hole, passes will initially seem better: having milder winter (and less hot summers forecast) as ABH, the N.H. is closer to the sun in winter by 11%.**
That causes a huge increase in ocean evaporation a, especially in the mainly ocean S.H., with about ten foot of snowfalls every winter day in the milder N. H. (Huge snow falls only happen in mild, near 0C weather and that is an every winter day occurrence with N.H, closer to the sun and winter tilted away from the sun still ~20 or so degrees.) When summer comes to the N. H. it is farther from the sun than now so much of the huge layer of snow fails to melt, starts transforming into glazer ice in the cooler weather.
** Book has an appendix giving the finite time step computer code for the solution to this "three body problem" (Earth, sun & BH). It all could be true. One chapter explains current causes of climate, why prevailing wind comes from the West, etc. and another on the ABH climate. As I said it is a physic book in disguise for those who don't want to ever read one. All of Keplers Laws are used in calculations, but never named - too much like teaching, which would turn my target reads off. One chapter speculates on what the small black hole might be. It of course can not be seen by telescopes. My favorite is a dense cubic crystal of magnetic monopoles - why none have every been found. I won't go into detail but the approach of the SBH can not even be detected by gravitational lensing effect as it is too close (moving too fast) wrt to the back ground stars.
Last edited by a moderator:
Yazata
Valued Senior Member
Motordaddy's question looks like a thoughtful and creative one to me. (Thinking and creativity are things to be applauded, not put down.)
If we divide a whole into two parts, we have two 1/2's, which equal the whole that we divided.
If we divide a whole into 374 parts, we have three hundred and seventy four 1/374's, which still equal the whole.
But if it's true that 1/infinity = zero, then that would seemingly imply that if we divide a whole into an infinite number of parts, then everything will somehow disappear into thin air.
I'm more inclined to think that we would still have an infinite number of infinitely small parts, which would still total the whole.
Maybe that idea is wrong, but the question is why.
Motor Daddy
Valued Senior Member
Well then explain to me why the .999...never includes the remainder, and yet you claim .999...=1. You fail to include a percentage of 1.0 in .999... and then you claim .999...=1? That is complete BS, Tach, and you know it!
Cranks like to think themselves as "creative", "out of the box thinkers"
You both think in elementary terms of integer division, this is not a problem reducible to integer division. This is why your ideas are wrong.
Motor Daddy
Valued Senior Member
Tach, Do you agree that .9 (90%) of a whole means there is .1 (10%) of the whole not included in the 90%?
How about .99? Do you agree that .99 means there is .01 not included?
How about.9999999999999999999999999999999999999999999999999999999999999? Do you agree there is a portion of the whole that is not included in the .9999999999999999999999999999999999999999999999999999999999999?
Why do you insist that .999... is NOT missing a piece but that it is the WHOLE? How do you justify that when a whole is 1.0 and a percentage of a whole has a zero in the ones position and a 9 in the tenths position? You know that .9 is less than 1.0. You know that .99999 is less than 1.0. You know that .999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 is less than 1.0. Then you have to know that .999... is also less than 1.0. You have to know that, otherwise you are the lunatic, not me!
How about .99? Do you agree that .99 means there is .01 not included?
How about.9999999999999999999999999999999999999999999999999999999999999? Do you agree there is a portion of the whole that is not included in the .9999999999999999999999999999999999999999999999999999999999999?
Why do you insist that .999... is NOT missing a piece but that it is the WHOLE? How do you justify that when a whole is 1.0 and a percentage of a whole has a zero in the ones position and a 9 in the tenths position? You know that .9 is less than 1.0. You know that .99999 is less than 1.0. You know that .999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 is less than 1.0. Then you have to know that .999... is also less than 1.0. You have to know that, otherwise you are the lunatic, not me!
That's all true.Motor Daddy said:
Here we see the application of finite-length decimals with the form 0.9(n) that are always less than 1, used as the premise for the argument that infinite length decimals with the form 0.9(9) are also always less than 1, without recognising that finite-length and infinite-length are NOT the same.
This appears to be coupled with an inability to see that there is no remainder in 0.9(9). Motor Daddy can't see beyond the method of long division, where the remainder from a step in the process is carried over to the next step.
If you can get your head around long division being an artificial method, or a way to prove that a number divides another number with or without remainder, and that the numbers still divide regardless of this proof method, you might be able to move on and see that this method will never complete with a repeating decimal, but that does not mean the numbers don't divide each other.
So a method of division isn't some kind of bound on whether a number is divisible by another number.
There is however, a practical bound. We can't build calculators or computers with infinite length registers. This does not mean repeating decimals don't exist (well, duh!).
Ok?
Motor Daddy
Valued Senior Member
You miss the point of division completely!
Dividing a whole (1.0) (100%) into 2 parts means there are TWO EQUAL PARTS of .5, or each part is 50% of the whole. The statement 2*.5=1.0 proves the division was successful and all is accounted for, the "all" being all of the whole, 100% of the whole is accounted for.
When you do NOT have a 1.0 as an answer to (number of parts*percentage of whole of each part) then you know your parts are not equal and don't total a whole 100%.
One divided by three means there are 3 parts of .333..., but 3*.333... does NOT EQUAL 1.0, so there is a piece missing, meaning there are actually 3 parts of .333... and one part that is the remainder that continues to be divided. The division continues, the remainder is never divided equally, and the total of the "3 equal pieces" is not 100% at any time, because there is a portion of the whole that is not included in that 3*.333...
You're saying 0.333... is not 1/3?MD said:
So then, 1/3 + 1/3 is not equal to 0.666...? But 1/3 + 1/3 is still 2/3?
How about 1/3 + 1/3 +1/3, is that 3/3, or what?
No, the division isn't done in steps, it's immediate.
You're stuck with the idea that there is one and only one way to divide 1 by 3, long division, and this is always done in steps, because, well, it just is!
Motor Daddy
Valued Senior Member
3/3=300%/3
1/3=100%/3
Do you know the difference between the two? Evidently you don't.
1.0=100%
3.0=300%
You are saying 3/3=300%/3=100%, and I agree!
You are also saying 100%/3=33.333...%, and I agree!
I am saying 3*33.333...=99.999...% which is less than 100%, and you are disagreeing. Your ignorance is baffling you and you take that to be that I am baffled, but again, truth is not relative. Truth is absolute!
What is "immediate" about .999...? You have a REPEATING DECIMAL, so the operation is continuously repeating and never complete, rate of repeat being irrelevant!