Does this mean you can't or won't answer the direct questions I put to you above?
I thought so.
It must be possible to reconstruct 1 out of 9 x 1/9, surely?
Are you saying it can't be done?
1=0.999... infinities and box of chocolates..Phliosophy of Math...
- Thread starter Quantum Quack
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Does this mean you can't or won't answer the direct questions I put to you above?
I thought so.
It must be possible to reconstruct 1 out of 9 x 1/9, surely?
Are you saying it can't be done?
In other words, you can't understand a mathematical proof when you're given one. Or at least not this particular one.
Unfortunately, you picked a bad subject to waffle on about. Mathematics is just about the most rigorous, logical subject there is. It's also one of the only subjects in which complete proof is possible, given a set of agreed axioms. The syntax of mathematics is the way that it is written concisely and without room for misinterpretation. Without the syntax, you can't hope to understand the maths.
What you see in post #915 is a proof that 0.999... = 1.
Your only response to that is to say "I don't understand mathematical proofs. But I have this feeling that it can't be true that 0.999... =1, so my feeling must be right regardless of what any proof says."
And then we're back at home in Motor Daddy Fantasy Lala Land again, where the only things allowed to be real are the dreams of Motor Daddy.
Motor Daddy
Valued Senior Member
You can't divide a pizza into 3 EQUAL pieces. You AUTOMATICALLY ASSUME that you can, but you can't. If you say you can, then tell me what the size of the 3 equal pieces are that total 100%?
Motor Daddy
Valued Senior Member
No. You don't CONSTRUCT 1, you DIVIDE a whole 1 into equal pieces. If those pieces can't be divided equally, then ... is your method of saying it broke down.
Motor Daddy
Valued Senior Member
Right. That's why I'm here trying to explain my method in real...English....words. If you happen to understand my English, and you agree, then you can do the math and see for yourself!
Each piece is one-third of the pizza.
And you're saying that, once divided, you can't put it back together again, eh?
What's the problem with dividing something into thirds? Or nineths? Or halves, for that matter?
Do you think it is possible to divide a pizza into 2 equal pieces? How about 4?
And what about 3 or 7 or 9 or 10?
If some of these are possible and some aren't, you need to explain why. What's the general principle at work?
But rpenner already did the math that proves you wrong - back in post #915, above.
That's the game ender for this thread. The rest is just waffle from people who can't follow the proof.
Look - I'm willing to walk you through the proof step by step if you like. Just ask questions about what you don't understand.
Go on. Show me you're willing to learn something. I dare you.
Motor Daddy
Valued Senior Member
No James, we started with 100%, and you need to tell me what percentage of the pizza each piece is. The total MUST be 100%, not 99.999%
No, I'm saying you never finished dividing it, because the operation never completed, because the whole can't be equally divided into that many EQUAL pieces.
Motor Daddy
Valued Senior Member
I'm willing to learn how you divided 100% into 3 equal pieces with no remainder?
I dare you!
Game over for you, and you never made it out of the locker-room.
Motor Daddy:
You forgot to answer the following questions I put to you:
Please don't forget again when you post your next response.
Each piece is 33 and one-third percent of the pizza, of course. And (33 and one-third) times 3 equals 100%.
You forgot to answer the following questions I put to you:
James R said:
Please don't forget again when you post your next response.
Each piece is 33 and one-third percent of the pizza, of course. And (33 and one-third) times 3 equals 100%.
Motor Daddy
Valued Senior Member
Yes, a pizza can be divided equally into 2 pieces, or 4 pieces.
If the division ends in ... then it's no good. It's BS. It's throwing the last remainder away and calling it 100%, and that is cheating, James. You aren't allowed to throw away ANY of the whole 1. Don't you know you are sweeping a small piece under the rug when you claim ... is complete 100%?
Done. The general principle is that if the division doesn't complete, then you put a ... at the end, which means, "THIS IS BS."
what is the 1/3?
News Flash! Read all about it!
Motor Daddy declares that cutting a pizza into thirds is impossible!
Pundits wonder whether this theorem might be extended to pieces of wood, piles of sand, the Empire State Building and the three-term school year.
Or this:
----
There are 24 hours in a day. Suppose I were to try to divide the day into 3 equal periods of time. Motor Daddy tells us this is impossible!
And yet, it seems to me that three periods of 8 hours each would add up to 24 hours in total. Look:
(one-third of a day per day) times 24 hours = 8 hours.
Alternatively, I could start by dividing an hour into 3 equal periods of 20 minutes, then multiply by the number of hours in a day:
(20 minutes per hour) times 24 hours = 8 hours.
But wait! What if I start by dividing each minute into equal periods of one-third of a minute?
(20 seconds per minute) times (60 minutes per hour) times 24 hours = 8 hours
What if we divide each second into three equal periods?
(0.333... seconds per second) times (60 seconds per minute) times (60 minutes per hour) times 24 hours = 8 hours.
Motor Daddy declares that cutting a pizza into thirds is impossible!
Pundits wonder whether this theorem might be extended to pieces of wood, piles of sand, the Empire State Building and the three-term school year.
Or this:
----
There are 24 hours in a day. Suppose I were to try to divide the day into 3 equal periods of time. Motor Daddy tells us this is impossible!
And yet, it seems to me that three periods of 8 hours each would add up to 24 hours in total. Look:
(one-third of a day per day) times 24 hours = 8 hours.
Alternatively, I could start by dividing an hour into 3 equal periods of 20 minutes, then multiply by the number of hours in a day:
(20 minutes per hour) times 24 hours = 8 hours.
But wait! What if I start by dividing each minute into equal periods of one-third of a minute?
(20 seconds per minute) times (60 minutes per hour) times 24 hours = 8 hours
What if we divide each second into three equal periods?
(0.333... seconds per second) times (60 seconds per minute) times (60 minutes per hour) times 24 hours = 8 hours.
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Motor Daddy:
You asked above:
I ask you: what is 1/2 a percent? Or 1/5 of a percent?
Why do you think it is possible to divide a pizza into 2 pieces, but not 3? Can't I get out my knife and cut three equal pieces, in principle?
Is it really impossible to have one-third of a pizza?
If so, why is is possible to have half a pizza?
And is one-fifth of a pizza a possibility?
Why is one-half ok, and one-quarter, but not one-third?
You asked above:
MD said:
I ask you: what is 1/2 a percent? Or 1/5 of a percent?
Why do you think it is possible to divide a pizza into 2 pieces, but not 3? Can't I get out my knife and cut three equal pieces, in principle?
Is it really impossible to have one-third of a pizza?
If so, why is is possible to have half a pizza?
And is one-fifth of a pizza a possibility?
Why is one-half ok, and one-quarter, but not one-third?
Let me just refine my time argument above, to make it succinct:
I say that one day can be divided into three equal time periods of 8 hours each.
Motor Daddy, on the contrary, says that division of anything into thirds is impossible, because there is always a piece "left over" after the division.
My question to Motor Daddy: After I divide the day into three equal time periods, how many minutes or seconds or fractions of seconds are left over?
I say that one day can be divided into three equal time periods of 8 hours each.
Motor Daddy, on the contrary, says that division of anything into thirds is impossible, because there is always a piece "left over" after the division.
My question to Motor Daddy: After I divide the day into three equal time periods, how many minutes or seconds or fractions of seconds are left over?
To other participants in this thread who think that 0.999... doesn't equal 1:
Are you willing to join Motor Daddy in his claim that it is impossible to cut a pizza into three equal pieces, even in principle?
Or are you all going to cut him loose at this point, to go it alone?
Are you willing to join Motor Daddy in his claim that it is impossible to cut a pizza into three equal pieces, even in principle?
Or are you all going to cut him loose at this point, to go it alone?
Motor Daddy
Valued Senior Member
Old news. You're a day late and a dollar short. What do you think I've been saying all of this time?
Whoa, hold on there. We are not talking about dividing 24, we are talking about dividing 1. Do you know the difference? Evidently you don't, James, or you never would have said that.
1 day is 24 hours.
If I can divide 24 hours into three pieces, each 8 hours long, then I can equally divide a day into thirds of a day, each 8 hours long.
I conclude from this that it is possible to have one-third of one day. This is equivalent to a period of 8 hours.
We can represent this in several ways. For example:
8 hours = 1/3 day = 0.333... days = 480 minutes = 1/21 weeks = 0.047619 047619 047619 ... weeks = 28800 seconds.
It looks to me like we can divide a day into 3 equal pieces, and a week into 21 equal pieces, and this is not a problem even though 1/3 and 1/21 have infinite decimal expansions.
Do you still want to argue that ONE day can't be divided into 3 equal parts?
If I can have a third of a day, why can't I have a third of a pizza?
Motor Daddy
Valued Senior Member
1 day=100%. 24 hours=2,400%
We are dividing 100% into pieces, not 2,400% into pieces.
Wrong. We are not dividing 24 hours into piles of hours, we are dividing days into piles of days. You are digging, James. Quit digging!
I conclude that you've never understood a word of math, since 1st grade.
100% of 1 day is 24 hours.
Yes. I divided 1 day into 3 piles of third-of-a-day.
One-third of a day is 8 hours.
Do you agree?
If not, how long is a third of a day?
Or do you think that it's meaningless to speak of a third of a day?
Can you have half a day? How long would that be? What about one-tenth of a day? Is that possible?
Any ideas how long half a day would be, Motor Daddy?
You're woefully equipped to judge such things. Previously, you admitted you couldn't understand post #915, above. And you have no response to my post about the representation of fractions such as one-third in bases other than decimal.
In fact, you seem to ignore almost all of the substantive arguments I put to you.
Are you really this stupid, or is this all just a ploy to pass the time?