That’s what you have to prove. You should keep that for the end of your post instead of stating it this early.
Alright, so you’re stating your position one more time. I am not sure why.
Cool, so now you’re explaining to us how long division works. And this is somehow supposed to prove your point?
Basically, all you’re doing is insisting that if 1/3 has no decimal equivalent that it follows that a whole cannot be divided into three equal parts. You have said that before – too many times, in fact. So you aren’t really saying anything new. You are merely repeating yourself.
If it doesn’t have a decimal equivalent it’s because the division can’t be divided equally. If it can’t be divided equally then you can’t have equal pieces.
Take your bananas example. 1 group of bananas can’t be divided into 3 equal parts. You would end up trying to divide 1 Group into 3 equal parts, which can’t be done! If you say 1/3 of a group of bananas is 1 banana then what you did is divide 3 bananas into 3 parts, so each part is 1 banana. We are not talking about dividing 3 bananas into 3 parts, we are talking about 1 GROUP divided into 3 parts, so each part is .333… group, not 1.0 banana. You are making the same mistake as obsrvr when you claim you divided 1 group into 3 parts and 1/3 is 1 banana. 1 divided by 3 is not 1.0!
You don’t seem to acknowledge that if there isn’t a decimal equivalent then there can not be equal parts.
You see how 1 divided into 4 parts means each part is exactly .25, and the 4 parts add up to 1.0??
If you can’t divide it equally into that number of parts then you can’t have that many equal parts! Simple.
What you are doing is claiming you can divide 1 group of bananas into 3 equal parts.
You acknowledge that 1 group of bananas divided into 4 parts means each part is .25 of a group, and not 1 banana, right? Then why on earth would you think you end up with 1/3 of a group being 1 banana??? What you are saying is that 1 group divided by 3 equals 1.0. That is nonsense! …and certainly you don’t mean that if there are 3 bananas in 1 group that 1/3 of a group is .333… banana!
Long division is merely a means to find an equivalent expression – assuming that it exists.
It can be done, as I just explained. Take ONE group of items that contains exactly three items and DIVIDE it into THREE sub-groups. Is that possible or is it not? You know very well that it is. Thus, we have SUCCESSFULLY divided a whole into three equal parts.
Or, since you like pennies so much, take ONE group of pennies that contains exactly 99 pennies and divide it into THREE sub-groups of pennies. Is that possible or is it not? You know very well that it is. Thus, we have SUCCESSFULLY divided a whole into three equal parts.
Your argument is merely that, because we can’t express the ratio using decimal numbers (even though we can express it as “third” or “1/3”), it follows that the above isn’t true. Really?
I am not talking about the decimal equivalent of 1/3. I have already said that there is no such thing. I am merely showing you that there are wholes that can be divided into three equal parts. Your claim was that there are no such wholes. Well, obviously there are. That’s what’s being disputed here. ONE group of three bananas can be SUCCESSFULLY divided into THREE equal parts – each part being a single banana.
As I said earlier, you fail to realize that the base-10 system is merely a language and a limited one at that i.e. one that you can’t use to talk about anything you want. It’s a language that has no word for “one third”. That’s pretty much it. And I’m sure that you agree that if a language can’t express something that it does not necessarily follow that that thing doesn’t exist.
Thirds do exist. One banana is a third of a group of three bananas. Take one banana, take another banana and another one. Then put them together. What do you get? You get ONE group of three bananas! See how these three individual bananas add up to one group of three bananas?
That’s indeed nonsense, but fortunately, that’s not what I’m saying (:
I’ll just respond to this since it sums up your mistake, which is the same mistake that obsrvr makes.
The unit is group, not banana. You have 1.0 GROUP, and you want to divide the GROUP into 3 equal parts.
What you are claiming is that 1 group divided into 3 equal parts equals 1.0 banana. I remind you that the unit being divided is GROUP, not BANANA.
As I explained to you before but you failed to understand, 1.0 group divided into 4 equal parts means each part is .25 group, not 1.0 banana, so why would you think dividing 1 group into 3 equal parts equals 1 banana?
It’s the exact same mistake that obsrvr makes. The unit is GROUP not banana. You are trying to divide 1 group into 3 equal parts that have the same unit GROUP.
You agree that 1.0 group divided into 4 equal parts means each part is .25 of a group, right? You agree that 4 parts of .25 group equals 1.0 group? Right? So WHY would you make some weird mistake when dividing the group into 3 parts?
Why all of a sudden the unit changes to banana and you end up with 1.0 banana instead of .333… group?
If you were dividing 300 bananas into 3 equal parts, each part would be 100 bananas. See how the unit stays the same?
If you were dividing 1.0 Inch into 2 equal parts then each part is .5 inch. See how the unit stays the same?
If you were dividing 1 gallon into 2 equal parts then each part is .5 gallon. See how the unit stays the same?
Then WHY ON EARTH would you claim dividing 1 group into 3 parts equals 1.0 banana???
— so why do you believe that 1/3 = 0.3333…?
1/3 = 0.3? No!
1/3 = 0.33? No!
1/3 = 0.333? No!
1/3 = 0.3333? No!
1/3 = 0.33333? No!
1/3 = 0.333333? No!
and on and on
No matter how many 3’s you add to 0.333… it will NEVER be equal to 1/3. Never!
Add 3 of the 0.333… and what do you get = “0.999…” right?
Add 3 of the 1/3 and what do you get = “1.0”
I wonder if motor daddy has ever managed to troll someone into accepting base 10 supremacy before. He’s very dedicated, for a troll. Maybe he’s not a troll and he really is just a proselytizer for base 10 supremacy, but… I’ve never actually seen him explicitly state as much, so maybe not. Maybe just a troll.
If we really did have a base 10 supremacist in our midst and not just a troll, I’d like to see some actual arguments for it. But the way he’s conducted himself in all of these discussions, constantly arguing in bad faith and insulting anyone who doesn’t agree with him, he must be a troll.
I’m not sure what you mean by this. The WORD decimal implies base 10, but you can certainly have numbers with a period in between, like 0.1, in other bases. Calling that number a “decimal” might not be the correct thing to call it, but it’s certainly possible to have numbers that look like that in other bases, and the value would be different in other bases than the value of 0.1 in base 10.
For example, (0.2 in base 6) is perfectly equal to 1/3
We don’t have to call them decimals then, so that way the concept of ‘numbers after a radix point’ doesn’t get confused for having any inherent relationship to the number 10.
So, it somewhat confusingly refers to any number of the form 0.x as a “fractional number”, even in other bases, but the dot is referred to as a radix. So I’ll just refer to them as ‘radix point numbers’ instead of ‘decimals’ – and there we go, we’ve linguistically divorced the concept of a dot in a number from the idea that it is somehow inherently related to base 10. Because it’s not.
I mean, assuming he’s not a troll. Which I still don’t assume. Many pages of bad faith arguments of course leaves me with only one rational assumption.
Exactly. That’s what I am saying. One banana is one third of a group of three bananas. In other words, the number of bananas in one banana is one third of the number of bananas in a group of three bananas. For some really strange reason, you are fixating on the number that stands next to the word banana. Don’t do that. I am NOT saying that one third is one.
What does “1/3” really mean? Don’t give me that vague “1 of 3 parts” answer. “1/3” is another expression for “one third” which is another expression for “three times smaller”. “One third of” then means “three times smaller than”. When you say that such quantities do not exist, you are saying that there is nothing that is three times smaller than something else. When you say that there is no whole that can be divided into three equal parts, you are saying that there is nothing that is three times smaller than something else. And yet, a single banana is three times smaller than a group of three bananas. And one foot is three times shorter than three feet. These things are three times smaller than, one third of, other things.
“One banana” is not an expression that is equivalent to “one third”. Neither is “one”. But one banana is a physical object that is one third of, or three times smaller than, another physical object – a group of three bananas. We have a whole (“a group of three bananas”) divided into 3 equal parts (each part being “one banana”).
One group of four bananas divided into 4 equal parts is indeed equal to 0.25 groups of four bananas but it is also equal to 1 banana. Both are correct. They are merely different expressions utilizing different units.
There are 100 centimeters in 1 meter. Thus, 0.01 m is equivalent to 1 cm. Similarly, “one third of a group of three bananas” is equivalent to “one banana”. What you’re doing here is you are begging me to find an equivalent expression that uses decimal numbers and “a group of three bananas” as a unit. There is NO such expression. And the fact that one does not exist does not mean that we can’t divide a whole into three equal parts. If that were true, then “one banana” wouldn’t be one third of “a group of three bananas”. And yet, it IS.
Because it’s not a mistake, let alone a weird one, but a point that you fail to get thanks to your obsession with decimal numbers.
One of the reasons is because the result isnt “0.333~ groups of three bananas”. The main reason is because I am trying to show you that the result exists – that result being “one banana”. One banana is one third of a group of three bananas. What doesn’t exist is an expression utilizing base-10 numbers and a group of three bananas as a unit.
And let it be known that you are not merely asking me to use “a group of three bananas” as a unit. You’re also asking me to use decimal numbers. In fact, decimal numbers are WAY MORE important to you. I could have said the result is “1/3 groups of three bananas” but you wouldn’t have accepted that because “1/3” is not a base-10 number. I could also have said the result is “(0.1_3) groups of three bananas” but that’s utilizing a base-3 number and not a base-10 number. You really are attached to your 10 fingers – and that’s all there is to say on this subject.
I’ve just realized a weird paradox of his banana example, haha. I’ll try to lay it out clearly.
He believes you can divide things in half, or in quarters, just fine.
So if we start out with a group of 4 bananas jjjj, we can divide that in half to have two groups of two jj/jj. And we can divide each of those new groups in half to have 4 individual bananas. He’s got no problem with that, and neither do we.
Now physically, this implies that when you split in between the bananas, that place where you’re splitting it is perfectly between the bananas, right in the middle, leaving both sides perfectly equal.
So in a group of 4 bananas, there are 3 “splitting points”, and if you split along all 3 points, he is totally fine apparently with the idea that all 4 individual bananas that come out are equal.
Now instead imagine, instead of splitting in half, you try to take one at a time. So you take the first one, j j j / j. Now he has no problem splitting one off, 1/4 is 0.25 which he’s expressed before is totally fine. But now, you’re left with a group of 3. jjj. Here’s the paradox. You see, the 2 remaining “splitting points” are in exactly the same place relative to the remaining bananas that they were before. Splitting the one banana off hasn’t moved those splitting points. And since we’ve established that the bananas between each splitting point are perfectly equal, there’s no logical reason why you can’t continue splitting these bananas off. BUT they’re now a group of 3, not a group of 4, so he would insist that now, for some strange bizarre reason, you can no longer split off an individual banana from this group of 3 - regardless of our previously established sense of equality between the splitting points.
What an artful troll, creating exciting paradoxes for us to discover
I don’t know of any quantum physics freaks who think that infinite decimals are impossible. Quantum physics I believe has a hard reliance on continuous mathematics.
You are claiming that you can start with 1 group and end up with 3 groups. That is total nonsense! You are claiming you can divide 1 dollar and end up with 3 dollars!
Don’t you see how much nonsense that is? But you CONTINUE to make that same mistake, over and over!
