# The Squared Circle

What happens if I accidentally divide one pizza into three equal parts, purely by accident. Would we have to stop using math?

I will repeat again, 1.0 is TEN TENTHS.
.999... is NINE TENTHS AND SOME CHANGE!
No, 0.999... is equal to 1. Repeating something that is incorrect does not make it correct.

It is accurate to 2 decimal places, 1.77... which is CLOSE ENOUGH! It is DAMN CLOSE! It is within .005 units. It is only 5 parts of 1,000 parts too long. That is CLOSE ENOUGH!

You can't make it perfect because there is no finite pi, therefore no finite circle area, therefore no finite square side length
POST 87
YOU ARE NOT ALLOWED TO SWEEP THAT REMAINDER UNDER THE RUG and call it good at .333...
POST 106 - Like someone did in POST 87 ???

There seem to be two failures in this thread:
1. Not accepting that 0.9999....(ad infinitum) = 1. It's not a matter of being "quite close", but exactly 1.
2. Not ignoring Motor Daddy for the troll that he clearly is.

Until those failures are corrected, this thread, and likely many like it, will just go from the bizarre to the ridiculous. Good for a quick read and a chuckle every now and then, I guess.

What happens if I accidentally divide one pizza into three equal parts, purely by accident. Would we have to stop using math?

What percentage would those parts be?

Good for a quick read and a chuckle
Or bemoan the failure of whatever education MR was edumacatted under

Or just bemoan MD being a troll

What percentage would those parts be?
0.33.....down to Plank scale level

0.33.....down to Plank scale level

.333... is not 1/3.
.333... is 33.333...%
.333 x 3 = .999
.999 + .001 = 1.00
.9999999999 + .0000000001 = 1.0
.99999999999999999999999999999999999999999999999999 + .00000000000000000000000000000000000000000000000001 = 1.0

You can not finish the division of 1 divided by 3, because there is always a remainder of 1 that remains to be divided in order to complete the division. The remainder is not part of the answer.333... so it is not part of .333... x 3 = .999...
.999... + the remainder = 1.0
1.0 - the remainder swept under the rug < 1.0

1/3 of 12 eggs is 4 eggs, and 4 eggs x 3 = 12 eggs.

1 dozen eggs divided by 3 is .333...dozen, and .333...dozen x 3 = .999...dozen, NOT 1 dozen.

Why doesn't it add up to 1.0 dozen? Because the best you can do is 3 parts of .333... and 1 part that is the remainder. That's 4 parts!

If you have 100 pennies, and 3 people, everyone gets 33 pennies (3 x 33 = 99) and there is 1 penny left (the remainder).

What you are claiming is that 99 pennies equals 100 pennies, and you pocket the other penny, and then claim everyone has 1/3 of 100 pennies!

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.333... is not 1/3.
Never said it was
By convention in the format - 0.333.....down to Plank scale level - the 5 dots are merely a filler until you arrive at Plank scale level where at the lowest level there is not always

always a remainder of 1 that remains to be divided in order to complete the division

At the lowest Plank scale level there IS NOT

********

In a sense, you could say that, even if we were to develop methods of measurements that took us down to these scales, we would never be able to measure anything smaller

https://futurism.com/the-smallest-possible-length

*******

Coffee time

Never said it was

If you think you divided 1 into 3 equal pieces that are each .333... then you are saying that .333... is 1/3 of 1.0. That is false.

You did not divide 1.0 into 3 equal pieces. You tried to divide 1 by 3 and quit with 3 equal parts and 1 unequal part. That's 4 parts, so you did not divide it into 3 parts.

.333
.333
.333
.001

add more 3's to the end of those and you have to add more 0's to the .001

.333333
.333333
.333333
.000001

Continue infinitely!

There are ALWAYS 4 parts!

What you are claiming is that 99 pennies equals 100 pennies, and you pocket the other penny, and then claim everyone has 1/3 of 100 pennies!

Continue infinitely!

There are ALWAYS 4 parts!

NO - NOT AT THE LOWEST PLANK LEVEL

Divide the pizza to the lowest Plank scale you WILL HAVE 3 equal parts

MATHEMATICS will allow you your infinity remaining 1

REALITY will not

NO - NOT AT THE LOWEST PLANK LEVEL

Divide the pizza to the lowest Plank scale you WILL HAVE 3 equal parts

MATHEMATICS will allow you your infinity remaining 1

REALITY will not

Are you gonna split an atom into 3 equal parts? How would you get all the electrons into 3 equal portions? How would you know you have equal electrons? How many electrons are there to split into 3 equal parts?

The bottom line is you are saying you can divide 1 electron into 3 equal parts. I am saying you can't, because 1 electron divided by 3 is 4 parts, .333..., .333..., .333..., and the remainder. 4 parts!

Are you gonna split an atom into 3 equal parts? How would you get all the electrons into 3 equal portions? How would you know you have equal electrons? How many electrons are there to split into 3 equal parts?

The bottom line is you are saying you can divide 1 electron into 3 equal parts. I am saying you can't, because 1 electron divided by 3 is 4 parts, .333..., .333..., .333..., and the remainder. 4 parts!

Now I get the big picture

I have stood behind persons like you appear to be in this thread

You want the check out person to count the sugar grains in the package to be counted and a signed statement from the packers that ALL packages have the same number

I'm out

Moving to another check out

Now I get the big picture

I have stood behind persons like you appear to be in this thread

You want the check out person to count the sugar grains in the package to be counted and a signed statement from the packers that ALL packages have the same number

I'm out

Moving to another check out

You are the one claiming you can divide 1 into 3 EQUAL parts. I am claiming that is BS!

1 divided by 3 can NOT be completed, so you CAN'T have 3 equal parts.

Again, in case you missed it:

.333
.333
.333
.001

4 parts that total 1.0

You are the one claiming you can divide 1 into 3 EQUAL parts. I am claiming that is BS!

1 divided by 3 can NOT be completed, so you CAN'T have 3 equal parts.

Again, in case you missed it:

.333
.333
.333
.001

4 parts that total 1.0
You heard it here folks! The troll says there is no such thing as 1/3!

You heard it here folks! The troll says there is no such thing as 1/3!

Troll, I already stated 1/3 of 12 is 4, but 1 dozen divided by 3 = .333... + a remainder, which is not 1/3 of 1.0

1 dozen divided by 3 = .333... + a remainder, which is not 1/3 of 1.0
Wrong. Again I must point out that repeating a falsehood over and over does not make it true. 1/3 = .333... whether you like it or not.

Troll, I already stated 1/3 of 12 is 4, but 1 dozen divided by 3 = .333... + a remainder, which is not 1/3 of 1.0
Wrong. Maybe by the time you finish writing all the threes it takes to replace those dots you'll have figured out why.

You accept, I take it, that fractions like 1/2, 1/4, 1/8 etc. can all be written as decimals with finite numbers of decimal places:

1/2 = 0.5
1/4 = 0.25
1/8 = 0.125
1/16 = 0.0625
etc.

Now consider the following series of sums:

1/2 = 0.5
1/2 + 1/4 = 0.75
1/2 + 1/4 + 1/8 = 0.875
1/2 + 1/4 + 1/8 + 1/16 = 0.9375
etc.

One argument that you made previously is that if we keep adding terms to any sum, it will keep getting bigger and bigger, without limit, because each "extra" term we add makes the result a little bigger than the one before.

Follow the above pattern, then. Consider:

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 +...

(Add as many terms as you like on to the end.)

My question for you is: will this sum ever reach 100, if we keep adding enough terms?
If that's too hard to work out, ask yourself: will it ever reach as high as 2?
Will it, in fact, ever reach as high as 1?

If the answers to all of these questions are "no", then it seems that we have found a counter-example to your claim that adding things to a sum always makes the sum bigger and bigger, so that eventually it will reach any number you care to name.

Mistake #2 is mistaking a finite sum (i.e. a sum with a finite number of terms) with an infinite sum.

Think about that same sum, where we just keep adding more and more terms, forever. A mathematician would write it like this:
$$\frac{1}{2} + \frac{1}{4} +\frac{1}{8} + \dots + \frac{1}{2^N}= \sum^N_{n=1} \frac{1}{2^n}$$

Those three dots '...' mean that we keep adding numbers until we get to the term with value $$1/2^N$$.

I assert that this sum, ending with n=N will always be less than 1, for any value of N you want to choose. If you want to try to dispute this, the easiest way will be to try to find a counter-example: a value of N which makes the sum greater than or equal to 1.

Now, mathematicians go a step further and ask: what happens as N "goes to infinity"? That is, if we could keep adding terms forever to the sum, what answer would we get? The answer is 1, for this sum. You should be able to see that this "makes sense", because the more terms we add to the sum, the closer the answer is to 1 (see the first few answers, above). There is a well-defined meaning of these kinds of "limiting processes" in mathematics, such that all mathematicians can agree on the "correct" answer (which usually matches "common sense", at least where the answers are finite).

Now consider the following sum:

S = 0.9 + 0.09 + 0.009 + 0.0009 + 0.00009 + ...

This sum, like the previous one, has answers for various N values (N is the number of terms, remember). Here are some of them:

N=1, S=0.9
N=2, S=0.99
N=3, S=0.999
N=20, S=0.99999999999999999999

You get the gist.

Notice how the higher we make N, the closer S gets to 1? So, we ask the obvious question: if we add an infinite number of terms, what answer do we get? Mathematically, what is S in the limit as N goes to infinity? This isn't a proof, as such, but the answer should be "obvious": the answer is 1.

Last point. Mistake #3 is in imagining that to find the number 1 as the "answer" to this last sum requires that a person actually spend an infinite amount of time. This is a mistake. We don't actually need somebody to sit with a calculator for a billion years adding the next "9" to the decimal, in order to see that the "final" result will be 1 (assuming the person sits there for long enough). We're smart human beings. We can see where this process is headed, without having to actually try to complete it.

Mistake #3 is a lack of imagination: failing to imagine that human beings are capable of comprehending infinity, and instead insisting that the human mind must remain forever stuck in the finite.

I would like to hope that there's something helpful for deniers of 0.999... = 1 (those three dots are shorthand for that sum, in the limit as N goes to infinity). However, I'm fairly sure that we had this same discussion on sciforums 10 or 20 years ago, with similarly helpful explanations posted back then. I think that, in 2022, those who were around back then and are still struggling to understand this will probably never get it. Those people should probably give up on advanced mathematics and let the mathematicians worry about such things for them, in future. Let the experts handle it, and don't worry your pretty heads!

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