No, and I didn’t imply otherwise.
The question was never what you were using, I have not ever questioned even once what base you were USING. I have questioned what the conversation was ABOUT, if it was about base 10, but I have never once questioned which base you were using.
To the contrary, all of my replies to you should make it quite clear that I know exactly what base you’re using. So I don’t understand the context to your question.
Then why bring up some other base when you didn’t think I was using another base. You knew exactly what I was talking about, but chose to muddy the water, which to me is dishonest and not sincere.
If you were truly sincere you would understand what I was saying and respond to the concept and not some tangential word game. You tried to manipulate the words, which is dishonest.
So I ask again, do you agree that 1 Dozen can’t be divided into 3 equal parts?
Then why bring up some other base when you didn’t think I was using another base
I didn’t bring it up because of what you were or weren’t using. I brought it up of my own volition, for my own reasons. Please read the place in the conversation where I brought up another base - read it carefully, and try to understand that I was not even remotely implying that you were using any other base.
I was using another base. I made a choice to use another base. Not you. I made that choice, I made it clear that I was making that choice, I even made it clear why I was using that base.
When I make a post in which I choose to use another base, there’s no reason to interpret my post as anything about what base you’re using. If I wear jeans, that’s not a claim that you are also wearing jeans.
Base 6 is not part of this conversation, so please refrain from using any other base in this part of the conversation, it just muddies the water.
For right now, we are using base 10.
12 Eggs is this many - 0 0 0 0 0 0 0 0 0 0 0 0
1 Dozen is this many - 0
We have already agreed that 12 eggs can be divided into 3 equal parts, each part having 4 eggs.
We are now talking about 1 Dozen.
Can 1 Dozen be divided into 3 equal parts? Yes or No?
Base 6 is not part of this conversation, so please refrain from using any other base in this part of the conversation, it just muddies the water.
No concept is part of a conversation until it is. If one of us decides that some particular concept is important to bring up for a point, then we’ll bring it up. If you decide to change the object of division from “eggs” to “chickens”, I’m not going to oppose that on the grounds that it’s “not part of the conversation”. That’s not fair, I don’t accept that you have the right to unilaterally decide what is or isn’t part of the conversation.
At the beginning of the conversation, percents weren’t part of the conversation. And then you brought up percents. I didn’t particularly like that you brought up percents, but I didn’t complain about it either. You’re allowed to bring up concepts you think are relevant to the conversation, and it would be acting in bad faith for me to disallow that.
If you’re making a claim specifically about base 10, and nothing outside of base 10, then you would possibly have grounds to tell me not to bring up other bases. But we’ve established that your claim isn’t about base 10, and since it’s not about base 10, if I have a relevant point to make that uses another base, I’m going to make that point using another base. I don’t agree to you having a monopoly on the parameters of the conversation - you can have a monopoly on defining the parameters of your own claims, but I will not just acquiesce and give you the right to determine what points I am and am not allowed to make. That is NOT the structure of a good faith discussion.
Can 1 Dozen be divided into 3 equal parts? Yes or No?
Yes I think so.
In base 10 (which I am using and speaking about) “One” or “1.00” or “100%” are all the same thing. There is no difference. “One” is a word for “1.0”, and 1.0 literally is 1.00, which is literally 100 Hundredths, which is 100%.
That is a totally different animal than changing bases. Nothing is changed between “One”, “1.00”, or “100%”, they all mean EXACTLY the same thing mathematically.
But as you have already acknowledged, in base 3 “10” is this many - 0 0 0
See the difference?
When I say “12” I am speaking about this many “0 0 0 0 0 0 0 0 0 0 0 0”
In base 3 “12” is this many “0 0 0 0 0”
To try to confuse the issue by switching bases is a dishonest tactic. We are speaking about this “0 0 0 0 0 0 0 0 0 0 0 0” not this “0 0 0 0 0”
Got it?
You think you can divide 1 dozen (this many “0”) into 3 equal parts (this many parts “0 0 0”) so explain in detail.
I want to know HOW MANY percent each part is, and I want to know HOW MANY dozen each part is?
Explain in simple terms using base 10.
It’s not my aim to confuse by switching bases, nor is it dishonest, it’s literally Central to my entire point of view on this conversation. You knew that coming in. There’s nothing inherently dishonest about disagreeing with you on this basis, when you say that your point is not ABOUT base 10 but that it merely uses base 10. It’s not dishonest, I’m not tricking you, I am upfront about it. This is my point and you know it’s my point.
My view is,
a) there’s no reason to prefer one base over another
b) 1/3 is perfectly representable in radix point form in other bases, so
c) 1/3 therefore shouldn’t be viewed to have the problems you think it has.
The only problems you can demonstrate with 1/3 are problems in base 10. I do not believe that base 10 is a fundamental part of reality, that it takes precedence over other bases. That’s precisely why I disagree with your claim. There’s nothing dishonest about my take. It is entirely honest. You may disagree with it, but it is not dishonest.
If you don’t want to engage with this point of view, you don’t have to. We can quit here. But this is my point of view, this is what you signed up for. If you only signed up for the express purpose to tell me “other bases are dishonest” then we’ve achieved everything we can here. Good job, you’ve achieved your goal, you showed me. But if that’s why you joined the conversation, then you’ve broken the agreement at the center of this conversation, because it wasn’t begun in good faith from your side.
If you did intend to talk in good faith, on the other hand, then you know this is my point of view, and so you’ll either engage with it, or end the conversation.
I’ve laid out my premises for my point of view. If your claim about 1/3 is not merely a claim about base 10, then I invite you to engage with my point of view honestly.
You said you think you can divide 1 Dozen into 3 equal parts in base 10. Where is your explanation?
We can talk about other bases after we conclude base 10 conversation. I am not trying to limit the conversation to base 10, only to keep the bases separate, as they should be.
For me to talk about “12” meaning this many 0 0 0 0 0 0 0 0 0 0 0 0 and for you to mix that with base 3 this many 0 0 0 0 0 is just not right.
Stick to base 10 unitl we have agreement, and then move on to a different base and we can discuss that independent of other bases. It is insanity to try to mix bases speaking about 0 0 0 0 0 0 0 0 0 0 0 0.
Why would you want such muddy water when trying to get to clarity on base 10?
Again, you said you think you can divide 1 dozen into 3 equal parts, so let’s hear it.
(1 Dozen) / 3, that’s how you do it
How many dozen is each part?
How many % is each part?
100/3 percent, 1/3 dozen
Do you know what I mean when I ask “how many?” I mean I want to know a number.
Say there are some apples on a table. I ask you how many apples are there. You respond with a number, right? You respond with something like “there are 12 apples on the table.” You don’t respond with the fraction 12/1.
“How many” is a word, like “twelve.” It is not a fraction. Do you count 1/1, 2/1, 3/1, 4/1, 5/1??? or do you count 1,2,3,4,5??
Now I am asking you HOW MANY (a number, not a fraction) dozen, and how many %.
If you must use a fraction for %, then I am asking you how many Hundredths is each part. An example would be 25/100 for 4 equal parts of .25 dozen each.
At the beginning of the thread, we had this discussion. I clarified that I don’t agree with you that fractions are not numbers, and that some fractions are not representable in base 10 as finite decimals, but are only able to be approximated by such notation.
My position on those things has not changed. You can approximate 1/3 as .3333… , But 1/3 itself is an acceptable answer as far as I’m concerned.
Let’s magnify the situation so we can see clearly what is going on.
Let’s try to divide 10 eggs into 3 equal parts. The first step is easy, each part has 3 eggs, and there is 1 remaining egg. So 4 parts so far, 3-3 and 1-1, for a total of 10 eggs. Agreed?
So we have 4 parts so far, 3 parts are equal, and the other part is not like the others. Agreed so far?
Yeah that looks fine so far
Good. So now all we have to do is divide the remaining 1.0 (100%) egg into 3 equal parts. Again, 30% for each of the 3 parts totaling 90%, with a remaining 10%.
So now we still have 4 parts, 3 of which are equal at 3.3 eggs (totaling 9.9 eggs) and the other oddball part that is .1 egg. Grand total 10 eggs (9.9 + .1)
Agreed so far that there is still 4 parts?
I agree that the way you’ve split it leaves it with those groupings, yeah.
I don’t know why you’re splitting it like that though, why not split the last egg into 3 equal pieces?
You can not split 100% into 3 equal parts, that is why the first split was 3 eggs for each part with 1 remaining part. If you could split it into 3 equal parts it would go no further than the first split.
Why didn’t you ask why I just didn’t split it into 3 equal parts at the beginning, because you know 3 x 3 =9, not 10? because you know 3.3 x 3 = 9.9?? Because you know 3.33 x 3 = 9.99?? and on and on?
We literally have 10 eggs, and the first split is 3 x 3 with a remaining 1. Now the division tries to finish by dividing that 1 into 3, which again means 90% and 10% left over. That goes on INFINITELY, so 10 eggs can’t be split into 3 equal parts.