1 is 0.9999999999999............

1 unit of minutes divided by 3 is equal to .333...units of minutes. You did NOT divide a unit into 3, you divided 60 units (seconds) into 3 which is 20 seconds. Do you know the difference between dividing 1/3 and 60/3? No! No you don't! Not even close, not by a long shot. Not even in the ballpark. You're somewhere out there in between totally lost, and knowing just enough to get yourself into trouble. When you find yourself stuck in a hole...quit digging!

So, when you go about dividing 30 (3 units of tens) by 2, do you go about it by saying "A ten for you and a ten for you. We now have a remainder of a ten."?

Of course not. What you do is you convert that remaining 1 tens unit to 10 units of ones and then divide those 10 ones by 2. So continuing, "Five ones for you and five ones for you. Nothing remains."

You know how to do long division, right? For 30 divided by 2, the 2 goes into the 3 (tens value) 1 time. 3-(2x1)=1

If we stay at just using the tens unit, we would have to stop here and declare that the answer is 1 ten with a remainder of 1. But we don't do this because the 1 remainder has the equivalent value of 10 ones in the ones unit. So we convert that remainder 1 to 10 and go ahead with the division, which results with 2 going into the 10 ones 5 times. 10-(2x5)=0

The remainder equals zero, so the result would be 1 tens and 5 ones = 15.

I did the same thing when dividing 1 minute by 3. Since 3 is too big to divide into 1 minute, I went the next unit down which is seconds. 1 minute has the equivalent value of 60 seconds in the seconds unit, so the 1 minute converts to 60 and then we divide by 3. The result is 20 seconds.

You're arguing that the next unit down from minutes is for some arbitrary reason supposed to be equal to one-tenth of a minute. That's not how the time units were setup, Motor Daddy. Just like how in decimal numbers the next unit down from the tens unit is the ones unit, the next unit down from minute units is the seconds unit. Sorry that you can't seem to grasp that simple concept.
 
I'm saying that your declaration of "One is not equally divided by three!" has been shown to be false even on your own terms because I revealed to you an example where 1 unit of something can, in fact, be divided by 3 without remainders since that 1 unit (minutes) is defined to be equivalent to 60 of a lower unit (seconds).

Now stop pestering me with your "equal to .333... minutes?" question that doesn't have anything whatsoever to do with the fact that a valid counter example to your declaration has been given. You just want to derail the conversation by attempting to trick me into saying there are remainders. As I have already shown in my example, of course, there are no remainders. :cool:

Now answer my question from post #889, because as it is, you are contradicting yourself by stating earlier that 0.999... - 0.999... = 0.


moni moni bo boni fee fie fo foni MONI! (Sorry couldn't resist. You have such a playful m-m-moniker :p)

I guess you've figured out by now that you're engaging some of the worst hacks to visit what purports to be informed discussion. I have most of the worst them on 'ignore' which filters the way the thread appears in my browser. It makes reading some of these exchanges rather funny, something like overhearing a phone conversation with someone arguing with, say, a senile person on the other end. Senile with an attitude, I should say.

Yeah you've stumped the chumps. Motor Daddy is somewhere among the most incorrigible of them, having devised a rather unique way of trolling the science threads with little or no checkmating by the mods.

Of course the reason that your example trumps all of his objections is that the conventional division of time into multiples of 60 already addresses the divisibility by 3 (as well as 2 and 5 and their multiples). He will get stuck on notation as fast as he gets tangled up in basic concepts. And man does that dude love to rail. Here he seems lost in the idea that division by 10 is magically somehow mo-bettah than dividing by any other number. If he had any clue that the decimal system is purely arbitrary, he'd realize that division by 3 would be just as matter-of-fact to him if he'd been raised in any of the cultures that used base-60 numbering as he seems to think division by 10 is, or whatever. (I think there is still an extant system that, when counting on their fingers, uses the three joints in each finger -- I forget how they treat the thumb -- to arrive at something like hexadecimal. Not sure really but obviously the primitive cultures would have had a chance to work out their own choices of a base.)

Anyhoo, you get my vote of confidence. What a nutty thread this is anyway. I didn't wade through the whole discussion but it sounds like it started off with some bad restatement of limits. Most folks won't agree that 1 = 0.999..., but rather, that the limit as (sum of 9 * 10[sup]-i[/sup]), as i goes from 1 to infinity, approaches 1. The symbol should be an arrow rather than an equals sign. And I'm giving this in prose form for the benefit of our resident 6th graders. It's that absence of a concept of an asymptote that eludes the folks who never made it past 6th grade math. As I recall Motor Daddy once admitted to being in that group. Needless to say, he's running berserk with the loose treatment of this subject, clearly unaware of the meaning of the phrase in the limit (among other things).

You wouldn't have any problem convincing me that 1/3 of a second is just as precise a statement of duration as 1/3 of a minute, or of an hour, but I suspect Motor Daddy will continue to spout more nonsense about it. But yours was a good example. Also interesting was Arfa Brane's mention of dividing a circle into three equal parts. Presumably Motor Daddy can divide 360 by 3 with ease and rest happy that it was equally divided. But try to teach him the meaning of radians and I suppose he will claim that the circle can not be divided equally.

From this kind of mental stumble-bummery he expects his readers to conclude that all of math (and science) is broken, which I presume is the world a few other perpetual 6th graders live in.

Notice how we can generate so many words out of the most elementary of concepts that are so concisely expressed in mathematical notation? Geez, at this rate the 6th graders won't get to 7th grade until they'e 90 years old. Someone better warn the old folks homes. They'd better not let their future residents see anything being counted out or divided up, or all hell will be breaking loose. Maybe by then insurance will cover injuries sustained during food fights. Who knows.
 
I did the same thing when dividing 1 minute by 3. Since 3 is too big to divide into 1 minute, I went the next unit down which is seconds. 1 minute has the equivalent value of 60 seconds in the seconds unit, so the 1 minute converts to 60 and then we divide by 3. The result is 20 seconds.

You're arguing that the next unit down from minutes is for some arbitrary reason supposed to be equal to one-tenth of a minute. That's not how the time units were setup, Motor Daddy. Just like how in decimal numbers the next unit down from the tens unit is the ones unit, the next unit down from minute units is the seconds unit. Sorry that you can't seem to grasp that simple concept.

What do you mean 3 is too big to divide into 1 minute? We are attempting to divide 1 minute into 3 equal percentages, each being an equal percentage, totaling 100%, with nothing left over.

.99 is a percentage of 1, 99% to be exact. .999 is also a percentage of 1, 99.9%.

.999... is also a percentage of 1, 99.999...%, which is not to be confused with 100%. 100% is a whole, and anything less than 100% is not a whole. Do you know the difference between 100% and 99%? How about 100% and 99.999%? How about 99.9999999999999999%? How about 99.999...%? None of them are equal to 100%! None of them! They are all LESS THAN 100%.
 
What do you mean 3 is too big to divide into 1 minute? We are attempting to divide 1 minute into 3 equal percentages, each being an equal percentage, totaling 100%, with nothing left over.

<WHIIIIIIINING IIIIN MY SKIIIIIN!!!!>

20 seconds + 20 seconds + 20 seconds = 1 minute

Undeniable FACT.

What was that about there not being 3 parts that all equal each other and sum up to 100% of 1 minute?

Once again, you're the one arguing that the next unit down from minutes is for some arbitrary reason supposed to be equal to one-tenth of a minute. How you can even tell time is a mystery.
 
20 seconds + 20 seconds + 20 seconds = 1 minute

Undeniable FACT.

What was that about there not being 3 parts that all equal each other and sum up to 100% of 1 minute?

Once again, you're the one arguing that the next unit down from minutes is for some arbitrary reason supposed to be equal to one-tenth of a minute. How you can even tell time is a mystery.

I ask you to divide a pie into 3 equal pieces, and you divide the damn thing into 60 pieces and make 3 piles of 20 each. Fine, each pile has 20 each, or each pile is 20/60, or 33.333...%. There is something amiss!!! Never can you get to 100% by adding the percentages of the piles up! Never!

UNDENIABLE FACT!
 
moni moni bo boni fee fie fo foni MONI! (Sorry couldn't resist. You have such a playful m-m-moniker :p)

Thank you! My younger sister chants the exact same thing to me sometimes when she greets me. :) Usually it's just Moni, though.

I guess you've figured out by now that you're engaging some of the worst hacks to visit what purports to be informed discussion.

I blame SIWOTI syndrome for my choosing to wade into arguing against the obviously inane repetitious posts.

I have most of the worst them on 'ignore' which filters the way the thread appears in my browser. It makes reading some of these exchanges rather funny, something like overhearing a phone conversation with someone arguing with, say, a senile person on the other end. Senile with an attitude, I should say.

Smart move. I should follow your example. Damn SIWOTI syndrome!

<flattering words>

Awww, thank you!! :eek:

(I think there is still an extant system that, when counting on their fingers, uses the three joints in each finger -- I forget how they treat the thumb -- to arrive at something like hexadecimal. Not sure really but obviously the primitive cultures would have had a chance to work out their own choices of a base.)

I'm not sure, but I think you may be referring to how to count in duodecimal (base-12) on one hand. Using the thumb as a pointer, you count each segment (three each) of each of your four fingers. If you have better finger control, then each of the fingers can be bent a certain degree for each segment count and you can use the thumb to hold a twelve count. So in just one hand you can count up to twenty-four! The duodecimal system would've made so much more sense!

Anyhoo, you get my vote of confidence.
:eek: again.

Also interesting was Arfa Brane's mention of dividing a circle into three equal parts. Presumably Motor Daddy can divide 360 by 3 with ease and rest happy that it was equally divided. But try to teach him the meaning of radians and I suppose he will claim that the circle can not be divided equally.

I agree that division of a 360 degree circle into 3 parts is a very good counterexample to Motor Daddy's statement, but we all know he's just not going to face it head on.

Anyway, I'm sticking with my minute/second argument to see how long this can go on for now.
 
I ask you to divide a pie into 3 equal pieces, and you divide the damn thing into 60 pieces and make 3 piles of 20 each. Fine, each pile has 20 each, or each pile is 20/60, or 33.333...%. There is something amiss!!! Never can you get to 100% by adding the percentages of the piles up! Never!

UNDENIABLE FALSEHOOD!

FTFY. You didn't ask me to divide a pie. Here's the quote of your "request":

What do you mean 3 is too big to divide into 1 minute? We are attempting to divide 1 minute into 3 equal percentages, each being an equal percentage, totaling 100%, with nothing left over.

.99 is a percentage of 1, 99% to be exact. .999 is also a percentage of 1, 99.9%.

.999... is also a percentage of 1, 99.999...%, which is not to be confused with 100%. 100% is a whole, and anything less than 100% is not a whole. Do you know the difference between 100% and 99%? How about 100% and 99.999%? How about 99.9999999999999999%? How about 99.999...%? None of them are equal to 100%! None of them! They are all LESS THAN 100%.

Nowhere does it have the word "pie" in it.

It's still undeniable fact that 20 seconds + 20 seconds + 20 seconds = 1 minute, and that 20 seconds are a third of 1 minute. So I still have shown that 1 of something can be divided by 3 without a remainder. Motor Daddy loses again, with an additional loss of credibility.
 
I ask you to divide a pie into 3 equal pieces, and you divide the damn thing into 60 pieces and make 3 piles of 20 each. Fine, each pile has 20 each, or each pile is 20/60, or 33.333...%. There is something amiss!!! Never can you get to 100% by adding the percentages of the piles up! Never!

UNDENIABLE FACT!

Trouble is, MD, that in 8-th grade geometry they teach you how to divide a circular disk (your "pie") into 3 equal parts using just a ruler and a compass. You and Undefined seem to have missed that class.
 
Trouble is, MD, that in 8-th grade geometry they teach you how to divide a circular disk (your "pie") into 3 equal parts using just a ruler and a compass. You and Undefined seem to have missed that class.

Trouble is, Tach, that when you attempt to make 3 equal pieces, the best you can do is make 3 pieces that are 33.333...% and have a remainder of the percentage left over, meaning there are 4 pieces, not 3. So you've failed to show how your 3 equal pieces total 100% of the pie and you've failed to divide the pie into 3 pieces. What you've done is to make 3 equal pieces and thrown the remainder (4th piece) away. Tisk Tisk, Tach, you know that's cheating, right? Your pieces may be equal but they do not total 100% because you threw the 4th piece away. Major problem with your math, eh?
 
So I still have shown that 1 of something can be divided by 3 without a remainder.

BS! All you've shown is that you can divide 1 minute into 4 parts, 3 of which are 33.333...% and 1 of which is the remainder that you are conveniently forgetting about. Did you forget that you never finished the division of 20/60? Did you forget that you quit dividing and just threw away the remainder (the missing 4th piece)?
 
There is a reason why Motor Daddy has been exiled to the darkness of Alternative Theories and Pseudoscience. But the above is a maximally obtuse position where he regards decimal percentages as more fundamental than either the arithmetic of division or geometry.
Thus $$\frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1$$, a statement which every 4th grade student is required to learn, is allegedly beyond his intellectual grasp. So by mental defect or outright trolling, Motor Daddy has announced to the world his inability to continue this discussion. We should all respect that and put him on ignore.
 
Trouble is, Tach, that when you attempt to make 3 equal pieces, the best you can do is make 3 pieces that are 33.333...% and have a remainder of the percentage left over , meaning there are 4 pieces, not 3.

Trouble is (for you) that that is not true since 8-th graders know how to divide the circle into three equal parts, no remainder.
Tisk Tisk, Tach, you know that's cheating, right? Your pieces may be equal but they do not total 100% because you threw the 4th piece away. Major problem with your math, eh?

Few ideas but fixed.
 
Trouble is (for you) that that is not true since 8-th graders know how to divide the circle into three equal parts, no remainder.

Equal what? Equal percentage of the area of the circle? The pieces may each be 33.333...% but that's not the entire circle. The entire circle is 100%, not 99.999...%, so you've done something with the remainder. What have you done with the remainder, Tach? Was it such a pain in the a$$ that you just carried the division out for a few decimal places and then decided that you were getting no closer to completing the task, and then you looked around to make sure no one was looking and you threw away the remainder and called it close enough? What you did is on par with Einstein's blunders. You've concluded that you couldn't figure out how to make the 3 pieces add up to a whole 100%, so you fab'd up some BS rule about .999...=1!

Bwahahahahahaha
 
Equal what? Equal percentage of the area of the circle? The pieces may each be 33.333...% but that's not the entire circle. The entire circle is 100%, not 99.999...%, so you've done something with the remainder. What have you done with the remainder, Tach? Was it such a pain in the a$$ that you just carried the division out for a few decimal places and then decided that you were getting no closer to completing the task, and then you looked around to make sure no one was looking and you threw away the remainder and called it close enough? What you did is on par with Einstein's blunders. You've concluded that you couldn't figure out how to make the 3 pieces add up to a whole 100%, so you fab'd up some BS rule about .999...=1!

Bwahahahahahaha

So your contention is that it is imposible to divide something into 3 equal parts? How about if you have 3 marbles in a bag and I ask you to remove 1/3 of the marbles? Is this impossible too?

Bwahahahahahaha, indeed.
 
Monimonika: Your Post #904 is a clever form of subterfuge (perhaps equivalent to lying). You essentially accuse me of claiming that 9/9 not equal to one.

At least you admit to snipping out part of my Post #901.

The part snipped provides a cogent reason for refuting a proof using the principles of elementary arithmetic.

As posted by me several times, I accept the various proofs using the limit of a geometric series, which is beyond the notions of elementary arithmetic.

It is proofs using elementary arithmetic to which I object.
 
It is proofs using elementary arithmetic to which I object.
And yet there is nothing wrong with such proofs as long as you play by the rules. One of those rules as Prof. Gowers explains in his definition is 0.999... = 1.000... but even if Gower's didn't assert that as the definition it follows as a consequence of 9.999... - 0.9999... = 9.000... (which MotorDaddy doesn't accept) or 0.999... - 0.00999... = 0.99000.... (which, perversely, MotorDaddy does accept).

https://www.dpmms.cam.ac.uk/~wtg10/decimals.html (h/t to AlphaNumeric for popularizing this link in the past.)
 
Good morning Monimonika, Motor Daddy, everyone. :)

Nowhere does it have the word "pie" in it.

It's still undeniable fact that 20 seconds + 20 seconds + 20 seconds = 1 minute, and that 20 seconds are a third of 1 minute. So I still have shown that 1 of something can be divided by 3 without a remainder. Motor Daddy loses again, with an additional loss of credibility.

My bolding above. That is why one should acquaint oneself with the background discussion (in this instance preferably both in this thread and QQ's contextually related Philosophy on Maths thread in the Philosophy section) before jumping into it with all guns blazing. If you read back you will see where the reality of dividing a real pie (and not just more trivial maths abstractions) is what it's all about now. It's about how does the maths operations go about relating to reality process/phenomena. :)

As to your 'equal three parts' division argument using minute and seconds, I already covered such trivial 'compositions' which make a-priori constructions by multiplication using a number and then trivially reversing that 'composition' by merely dividing by that same number.

See? One an construct endless trivial numbers composed of 3s (eg, 1 x 3= 3; 2 x 3= 6 etc etc) but that is not in the spirit of xamining the essentials of FRACTIONS like 1/3, is it? If one merely constructs and number and then deonstructs it trivially, then it is essentially a 'NON-action' which does nothing to explore the meaningful aspects/insights to be had by such examinations as MD is attempting to get you to do in that spirit of FRACTIONS process/operation in reality.

If you really want to take MD to task, then stick to treating the 1/3 fraction expression and explain what it means in reality and how that process results in (allegedly) 3 'equal parts'.

You especially need to consider (when diving 1 realm pie into allegedly three equal parts) what and how you are going to divide that CENTRAL POINT among the three SECTORS (axiomatically a 'point' in mathematics has NO dimensional extent, and so represents a central 'discontinuity' in the reality of that pie in reality?). This is the question, what happens to that central point? Which of the three sectors of real pie gets it? Or, how is NOTHING (a point without dimensional extent) to be SHARED among the three sectors in order to actually get 3 equal sectors? :)


Anyhow, whatever the discussion points presented, we should bear in mind that unltimately the real implications of the (maths/reality) treatments OF such 'central point' aspects has to do with the concept of REAL 'infinitesimals'; and how some 'infinitesimal of effectiveness' must exist which reflects the real process of change from one state to the next (ie, from 0 to non-zero; from infinity to finite and back again. Until such things are really made consistent with both the maths (for modeling) and with the reality (for meaningful comprehension), both the mathematics and the physics will remain INCOMPLETE.

In short, Monimonika, MD, everyone, it requires further 'bridging insights' into the mathematical/physical 'infinitesimal of effectiveness' before we can truly say we understand the universal phenomena consistent and complete. Hence these discussions here and elsewhere! Keep at it, guys....and enjoy it....and keep your cool. Cheers all! :)
 


As posted by me several times, I accept the various proofs using the limit of a geometric series, which is beyond the notions of elementary arithmetic.


That part is good, you accepted the proof I did via using the limit of the sum.


It is proofs using elementary arithmetic to which I object.

This part is wrong, since the proof using the fact that $$10*0.(9)=9.(9)$$ is equally correct. Think about it this way, multiplication by 2 in base 2 , in a computer, is done via a shift left by one bit. Multiplication by 10 of a periodic number, like $$0.(n)$$ in base 10 is done ALSO via a shift left, by one DECIMAL. In other words, $$10*0.(n)=n.(n)$$. Your "intuition" that the "correct" result is $$10*0.(n)=n.(n)0$$ is downright incorrect, the digit that is being "shifted in" from the right is NOT $$0$$ but $$n$$.
 
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