Ooops, I forgot the most important thing:
See how 1/128 = 0.0078125 = 0.78125%
Guess what 0.78125 % x 128 = ???
YUP, It’s 100%!! Not 99.999…%
Dude I knew that in second grade. What does this have to do with the theorem I posted or the topic in general?
Everyone on earth knows that terminating decimals can all be reversed to 100%
That’s not what this topic is about.
Flannel, thanks for the pm.
I know it’s not prime factorization … because different bases have different primes.
Nine in base 10 is not a prime number btw.
My theorem is simple.
1 under base.
All it’s equal divisors.
The the lowest denominator of this divisor subtracted from base.
Let x=0.9999…
10x = 9.9999…
= 9 +0.9999…
= 9 + x
10x - x = 9
9x = 9
x = 1
The mysteries of infinite series, baby!
For posterity sake, let it be known that Motor did indeed recognize that in base 3, “1/10” produced a valid non repeating decimal value, so in the end, he does think you can divide by 3. (He’s just unwilling to call it 3 now for some reason haha)
Just to add an additional opinion on the question of if 1 can be divided into 3 equal parts, this is what iAsk.AI has to say when asked:
Case closed! 
Emphasis is mine.
Noone is disputing the above. It is indeed true that there is no whole number that you can multiply by 3 and get 1. You can say the same about many other rational numbers e.g. 1/2, 1/4, 1/5, etc.
So nope, far from closed (:
AI isn’t the sharpest tool in the shed.
There also is no FRACTION that can be multiplied by 3 to get 1.0. That’s the point. One divided by three can’t be completed equally, so how could a fraction (or decimal) multiplied by 3 equal 1.0???
Don’t believe this link. Math is bad, not fun!
mathsisfun.com/numbers/natu … nacci.html
That’s not true. (\frac{1}{3}) is a fraction. When you take (\frac{1}{3}) and multiply it by (3) you get (1).
It is true that there is no base-10 representation of (\frac{1}{3}). However, there is a base-3 representation of the number. And if there is a way to represent a number, then the number exists. Thus, (\frac{1}{3}) exists.
Noone knows what you mean when you say “1 cannot be divided by 3”. Perhaps all you’re saying is “There is no way to represent 1 divided by 3 using base-10 notation”. That is true but the problem is that your statement is misleading; it can be very easily interpreted to mean that the result of 1 divided by 3 does not exist ( which is false. )
1/3 is a fraction, but there is no such animal as 1/3 of 1.0 because you can’t divide 1 into 3 equal parts. No 3 equal parts then no 1/3 of 1.0.
There is no number “3” in base 3, so there is no fraction 1/3 in base 3.
I mean literally that 1 can not be divided into 3 equal parts. If 1 can’t be divided into 3 equal parts then there is no such thing as having 1/3 of 1.0.
In base-3, (\frac{1}{3}) is represented as (0.1).
“1 divided by 3” in base-10 is “1 divided by 10” in base-3. And the result of that is represented as “0.1” in base-3. In base-10, there is no representation of that number.
Your entire argument so far has been that, just because there is no base-10 representation of “1/3”, it follows that “1/3” does not exist. That does not follow. If you do not have a word for something, it does not mean that that something does not exist.
If you slice 1 pie into three parts, they won’t be identical in size, even if you try for identical. You can only approximate.
Math is bad. Just slice up the pi & fricken enjoy it. I mean pie. Don’t ever let math stop you from sharing pie in a mostly fair way.
But you can divide 1 group of three pies into 3 individual pies. Doesn’t matter if they are equal in size or not. They are each 1 individual pie. And each individual pie is exactly one-third of the group of pies you started with.
I can bite into a .3333 (bar) piece of 1.0 pie?
Prove it.
There are different types of units. There are units of length ( e.g. meter, inch, etc ), there are units of volume ( e.g. m^2 ) and many other types of units. For example, when talking about how many people there are, the usual unit of measurement is “person”. Although people are physical objects that have properties such as volume, height, etc, the unit “person” does not refer to such properties. If you have two people in front of you, and the volume of one is twice the volume of the other, you don’t say there are 1.5 people in front of you, you say there are 2 people in front of you. Each person is exactly 1 person, regardless of their size. They are equal in this regard – they are equal in terms of how many people they are – regardless of their size. But what if your unit of measurement isn’t “person” but “a group of three people”? In that case, if there are 3 people standing in front of you, each person would be, regardless of their size, exactly 1/3 “a group of three people”. It is exactly true, not merely approximately.
In base 10 “1/3” is a fraction, which is equal to “1 divided by 3.”
In base 3 “1/10” is a fraction, which is equal to “1 divided by 10.”
In BOTH bases it is this many parts 0 of this many parts 0 0 0.
In both bases the 0 0 0 parts must be equal, and having 0 many parts of the 0 0 0 equal parts is what we are talking about.
In both bases 1.0 is the SAME.
In both bases we are talking about dividing 1.0 into 0 0 0 equal parts, and having 0 of those parts.
I repeat, you can not have 0 of those 0 0 0 equal parts of 1.0 because 1.0 CAN’T be divided EQUALLY into 0 0 0 parts.
We are not talking about starting with 0 0 0 parts and dividing it into 0 0 0 parts, we are talking about dividing 0 parts into 0 0 0 equal parts and having 0 of those 0 0 0 equal parts.
If you divide 1 GROUP into 3 equal parts you end up with 3 parts of a GROUP, and those 3 parts are each .333… of a GROUP, not each 1.0 pie.
The unit of measure is GROUP, not PIE.
If you start with 1 DOZEN and divide it into 2 equal parts you end up with 2 parts that are each .5 DOZEN, not 2 parts that are each 6. How could you divide 1.0 by 2 and end up with 6??? SHOW ME how 1/2=6???
They are not each “0.333… groups”. Rather, each part is “1/3 groups”. And they are also, at the same time, “1 pie”. They are not one or the other. They are both. It’s akin to “100 cm” and “1 m” being the same exact length.
Each part is “1/3 groups”. At the same time, each part is “1 pie”. There’s a reason why I’m emphasizing that they are each “1 pie”. The point is that they are real things. They are real pies. They are tangible objects that you can touch ( and even eat without getting sick or otherwise injured. ) And since each one of those pies is “1/3 groups”, we have a practical example of “1/3”. That’s the point.
You’re missing the point. I am trying to show you a real world example of 1/3. A real world example of 3 would be John, Peter and Mark. They are “3 people”. At the same time, each one of them is “1 person”. That would be a real world example of 1. Together, they are also “1 trio” where “trio” is taken to mean “a group or a set of three things”. That’s yet another example of “1”. And each person in that group is “1/3 trios”. That is a real world example of “1/3”.
The unit of measure “pie” does not enter the conversation. The conversation is about “group” and dividing that 1.0 group into 3 equal parts. NOWHERE does “pie” enter the math. You can’t start with 1 group and by dividing end up with a different unit of measure “pie.” One group divided by 3 does not equal 1.0 pie. That would mean 1/3=1, and that simply isn’t the case.
No it is not. You never finished dividing the group into 3 equal parts of the unit of measure “group.” We are dividing 1.0 group into 3 equal parts of group like we would divide 1 dozen into 2 equal parts of dozen. What you are saying is the equivalent of 1 dozen divided into 2 equal parts is 6 eggs. What you are saying is that 1/2=6, and that is WRONG.
Show me how 1/2=6?