1 Divided By 3

Philosophy Forums Science, Technology, and Math
1

We know that:

1/1=1 and 1x1=1
1/2=.50 and .5x2=1
1/4=.25 and .25x4=1
1/5=.20 and .20x5=1
1/8=.125 and .125x8=1
1/10=.10 and .10x10=1
1/20=.05 and .05x20=1

So what about 1/3??

1/3=.333… and .333…x3=.999… NOT 1

You know why? Because 1 can’t be equally divided by 3. The division never completes.

Do the long division of 1 divided by 3 and you will be on an infinite journey to complete the division equally, to which you will FAIL!

At some point you will see that you are in a repeating cycle of neverendingness, always ending up with the same remainder, to be be divided by 3, which continues endlessly, infinitely!

1.0 is 100%
.333…x3=99.999…%

100% is greater than 99%
100% is greater than 99.9%
100% is greater than 99.99%
100% is greater than 99.999%

And on and on and on. Infinitely!

2

But your logic only applies to the base 10 number system. It doesn’t apply to base three.

So 1 can be equally divided by 3, depending on what base you use?

3

I am speaking of base 10, yes. That goes without saying. 100% is 100 Hundredths (1.00). 50% is 50 Hundredths (0.50). 13.625% is 13.625 Hundredths, or 13,625 Hundred Thousandths, or 0.13625.

One pie is 100%, meaning 1 WHOLE pie. Dividing the pie into 3 equal pieces of 33.333…% means that the pieces only total 99.999…% of the pie, which you started with 100%.

You never completely divided the pie, otherwise the 3 pieces would total 100%. But they do NOT!

4

I don’t think it does go without saying. You said “1 can’t be equally divided by 3”. I don’t know if you mean “it can’t be divided equally by 3, only in certain bases” or “it can’t be divided equally by 3, period, ever”.

And you accept that if you use a different base numbering system, the 3 pieces would total 100%, right?

5

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Following, but not currently commenting.

6

Do you ask which base a person is referring to when they ask what percent of a pie they have if they half of the pie?
It goes without saying! We use base 10 unless otherwise stated. A Dime is 10% of 1 Dollar. A Quarter is 25% of 1 Dollar. A Half Dollar is 1/2 Dollar, or 50% (.50). It goes without saying!

In a different base system, how many pies is 10 pies??

7

My comment about bases isn’t about what base you’re USING, it’s about what bases your logic applies to.

Your logic only applies to base 10. It doesn’t apply to base 3. So when you say “1 cannot be equally divided into 3”, it’s ambiguous if you mean “1 cannot be equally divided into 3 in base 10” or “1 cannot be equally divided into 3 ever, period”.

Which one do you mean?

8

Let’s just stick with base 10 for now, shall we? You trying to muddy the waters to cover the problems in the base 10 system?

.1 means 1 Tenth
.01 means 1 Hundredth
.001 means 1 Thousandth

and so on

1.00 is 100 Hundredths
10.00 is 1,000 Hundredths
100.00 is 10,000 Hundredths

100% is 100 Hundredths, or 1.00
10% is 10 Hundredths, or 0.10
1% is 1 Hundredths, or 0.01

1 Pie is 100 Hundredths of a pie, or 100%, or 1.0

3 equal pieces of .333… only totals .999…, or 99.999… Hundredths, not 100 Hundredths that you started with!

9

So what?

10

So you can’t divide a pie into 3 equal pieces. That’s what!

11

I’m actually trying to clear the waters up. I’m trying to ascertain the nature of your claim.

Are you making a claim about the base 10 number system, or are you making a claim about reality?

Is it impossible to divide by 3 in base 10, or is it impossible to divide by 3 in reality?

12

Nice avatar, Motor Daddy! :smiley: =D>

13

I’m making the claim that in base 10:

300 Apples / 3 people = 100 apples per person and 100 x 3 = 300
30 Apples /3 people = 10 apples per person and 10 x 3 = 30
3 apples /3 people = 1 apple per person and 1 x 3 = 3

All good so far…

1 apple /3 people = .333… apples per person and .333… x 3 = .999…

and that is a big FAIL!

14

Thanks! :wink:

15

Oh, okay. It’s when you make comments like

That makes me think you’re making a claim about something more than the base 10 number system. That certainly sounds like you’re talking about reality, and not the base 10 number system. Since the existence of pies isn’t predicated on base 10.

16

In reality you can not divide 1 pie into 3 equal pieces.

1 pie is 100%, a whole pie. That is reality, that as we count, 1 pie is 1 whole pie, not 2 pies, or 7 pies, it is ONE WHOLE PIE!

We count 1,2,3,4,5,6,7,8,9,10,11,12,13…

Are you saying you are confused on how we count pies?

17

I’m saying I’m confused about your point about dividing a pie into 3 pieces.

Do you think you can divide a pie into 4 equal pieces?

18

See post 1.

1 pie divided into 4 equal pieces is 1/4=.25.

That is 4 EQUAL pieces of .25, and 4 x .25 = 1.0, or 100%.

So yes, you can divide a pie into 4 equal pieces, and the pieces total 100%

No on the 3! See?

19

Right, I’m glad I got this cleared up lmao.

So it seems like your idea about the impossibilty, in reality, of dividing a pie into 3 pieces is entirely based on the accident that you were born into a world where you were taught numbers using a base-10 system. If you were born into a world where you were taught numbers using a base-9 system, dividing pies into 3 would seem completely normal to you, but dividing them into 4 would be impossible.

I don’t think fundamental claims about reality should be based on the accident of what number-base counting system you use.

20

In any base system, 1 pie is the same. You can not claim that 1 pie would be different in a different base system. I am speaking about a pie, on the table. 1 pie, not 2 pies. Just one single lonely pie, on the table, waiting to be cut so that 3 people get the same pie. In our base 10 system that we use on a daily basis for money, and scientific data, 100% means A WHOLE! 1.0 Whole pie. We both know how many 3 people is, right?

So here’s what we have so far:

1 Pie
3 People
Everyone wants the same amount of pie. No cheating, and no feeding some to the dog!

With me so far?