You can think of a cake. You can divide a cake into 4 pieces or 2 pieces or basically not divide it, by ‘dividing’ it into 1 piece.
But it’s not possible to divide a cake into 0 pieces. It doesn’t make logical sense. You have to eat it (subtract from it) to actually make 0 pieces. With division, the sum of all pieces has to be 1 cake. If there’s one cake, there’s at least one piece.
What’s confusing is that we have separately decided that ‘dividing’ a cake into 0.5 pieces means you multiply it by 2. So, either 2 cakes or a cake that’s twice as large. That is why some mathematicians do treat 1/0 as ∞.
Its kinda interesting to me that math needs to fall back on the realm of language to express rhat which cannot be mathematically modelled, despite the fact that the structural format of the question inherently and one would conclude is more the question of numbers rather than words that undefined is inclusive of
Like, it makes total sense on an intuitive level and with a little rhetoric but it seems a little strange that on such a mathy issue, we need language (beyond the letters that algebra nominally requires) full-stop to express even what amounts to a non or undefined which is seemingly a more linguistic construct.
I mean, math really is just language. That’s why people argue over PEMDAS vs BODMAS and we have all those memes about “what’s the right answer to this arithmetic calculation?”
It just so happens that the math language we use is sufficiently refined to very closely reflect how things work in non-conceptual space (ie the Real World), often so much so that we can use it to get a new protective on that non-conceptual space and get insights about it that we didn’t have before.
Math and language are really both just symbols we use to describe the Real World; they’re basically the same thing.
I think you are really touching on math philosophy here. Is math discovered or invented?
Just because you can WRITE x/0 doesn’t mean you should be able to perform the operation. Because it’s conversion to language is non sensical (to you, at this moment) does heavily imply The operation is meaning or arcane.
You asked for a simple explanation of the math, so people analogized it into common language. That doesn’t necessarily mean the common language provided is a perfect mapping. The best answer for a math question will always be a math answer.
I think I’m all set, math pun intended and also I really appreciate your critique here 📐
Edit: i like that you brought up mapping since maps are in a similar sense only ever capable of representing something where distortion is inevitable even though irs fundamentally workable for the intended purpose
You mean that it’s undefined?
You can think of a cake. You can divide a cake into 4 pieces or 2 pieces or basically not divide it, by ‘dividing’ it into 1 piece.
But it’s not possible to divide a cake into 0 pieces. It doesn’t make logical sense. You have to eat it (subtract from it) to actually make 0 pieces. With division, the sum of all pieces has to be 1 cake. If there’s one cake, there’s at least one piece.
What’s confusing is that we have separately decided that ‘dividing’ a cake into 0.5 pieces means you multiply it by 2. So, either 2 cakes or a cake that’s twice as large. That is why some mathematicians do treat 1/0 as ∞.
Its kinda interesting to me that math needs to fall back on the realm of language to express rhat which cannot be mathematically modelled, despite the fact that the structural format of the question inherently and one would conclude is more the question of numbers rather than words that undefined is inclusive of
Like, it makes total sense on an intuitive level and with a little rhetoric but it seems a little strange that on such a mathy issue, we need language (beyond the letters that algebra nominally requires) full-stop to express even what amounts to a non or undefined which is seemingly a more linguistic construct.
I mean, math really is just language. That’s why people argue over PEMDAS vs BODMAS and we have all those memes about “what’s the right answer to this arithmetic calculation?”
It just so happens that the math language we use is sufficiently refined to very closely reflect how things work in non-conceptual space (ie the Real World), often so much so that we can use it to get a new protective on that non-conceptual space and get insights about it that we didn’t have before.
Math and language are really both just symbols we use to describe the Real World; they’re basically the same thing.
I think you are really touching on math philosophy here. Is math discovered or invented?
Just because you can WRITE x/0 doesn’t mean you should be able to perform the operation. Because it’s conversion to language is non sensical (to you, at this moment) does heavily imply The operation is meaning or arcane.
You asked for a simple explanation of the math, so people analogized it into common language. That doesn’t necessarily mean the common language provided is a perfect mapping. The best answer for a math question will always be a math answer.
I think I’m all set, math pun intended and also I really appreciate your critique here 📐
Edit: i like that you brought up mapping since maps are in a similar sense only ever capable of representing something where distortion is inevitable even though irs fundamentally workable for the intended purpose