# 1=0.999... infinities and box of chocolates..Phliosophy of Math...

Does this mean you can't or won't answer the direct questions I put to you above?

I thought so.

Anytime you see ... after a number you know the math broke down and it doesn't divide evenly. Remember when I talked about how it ALWAYS needs to total 100%? If the total is not 100% then the problem brings itself to life, as ...

It must be possible to reconstruct 1 out of 9 x 1/9, surely?

Are you saying it can't be done?

I can't answer that question, as I can't make heads or tails of the syntax.

In other words, you can't understand a mathematical proof when you're given one. Or at least not this particular one.

I don't place much importance on the syntax. It appears to me that some people care more about the syntax than the actual message.

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.

Right, so divide a pizza into 3 equal pieces and then join it up again... That doesn't equal a whole pizza?

You think that the act of dividing somehow removes an infinitesimal from the whole?
If so then why does this only work for certain divisions, then?

You'd surely accept that if you divide a pizza in half and rejoin it you'd get back to the whole, right?
1/2 + 1/2 = 1 and all that.

But because you can write it 0.5 + 0.5 = 1 it somehow doesn't lose the infinitesimal that you think 1/3 + 1/3 + 1/3 does?
0.333... + 0.333... + 0.333... = 0.999... = 1 etc.

Where do you think the infinitesimal goes?

I find it staggering that people can disagree with this notion.

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%?

It must be possible to reconstruct 1 out of 9 x 1/9, surely?

Are you saying it can't be done?

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.

In other words, you can't understand a mathematical proof when you're given one. Or at least not this particular one.

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!

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%?

Each piece is one-third of the pizza.

No. You don't CONSTRUCT 1, you DIVIDE a whole 1 into equal pieces.

And you're saying that, once divided, you can't put it back together again, eh?

If those pieces can't be divided equally, then ... is your method of saying it broke down.

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?

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!

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.

Each piece is one-third of the pizza.

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%

And you're saying that, once divided, you can't put it back together again, eh?

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.

Go on. Show me you're willing to learn something. I dare you.

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.

You forgot to answer the following questions I put to you:

James R said:
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?

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%

Each piece is 33 and one-third percent of the pizza, of course. And (33 and one-third) times 3 equals 100%.

Does any of the 0.999...-does-not-equal-1 crowd have any comments on the above post?

Or don't any of you understand that one, either?

Do you think it is possible to divide a pizza into 2 equal pieces? How about 4?

Yes, a pizza can be divided equally into 2 pieces, or 4 pieces.

And what about 3 or 7 or 9 or 10?

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%?

If some of these are possible and some aren't, you need to explain why. What's the general principle at work?

Done. The general principle is that if the division doesn't complete, then you put a ... at the end, which means, "THIS IS BS."

Each piece is 33 and one-third percent of the pizza, of course. And (33 and one-third) times 3 equals 100%.

what is the 1/3?

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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MD said:
what is the 1/3 [of a percent]?

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?

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?

Motor Daddy declares that cutting a pizza into thirds is impossible!

Old news. You're a day late and a dollar short. What do you think I've been saying all of this time?

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.

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.

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?

1 day is 24 hours.

1 day=100%. 24 hours=2,400%

We are dividing 100% into pieces, not 2,400% into pieces.

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.

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 from this that it is possible to have one-third of one day. This is equivalent to a period of 8 hours.

I conclude that you've never understood a word of math, since 1st grade.

1 day=100%. 24 hours=2,400%

We are dividing 100% into pieces, not 2,400% into pieces.

100% of 1 day is 24 hours.

Wrong. We are not dividing 24 hours into piles of hours, we are dividing days into piles of days.

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?

I conclude that you've never understood a word of math, since 1st grade.

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?