Sigh.
Yes. Obviously.
I just told you I would be glad to (in your words) “put to rest this joke of a conversation between the two of us” - not for the first time by any means(!), and each time you continue it or try to misrepresent me because you know I’ll respond to correct you. But no, as usual, you conclude incorrectly the first thing that pops into your head that it’s “ego issues” - I killed that a long long time ago. I just can’t stand stupidity being stupidly attributed by stupid people to people who are not stupid.
It’s not just a personal distaste, if others stupidly take stupidity seriously it can have a detrimental effect on many people, only fuelling the fire that is stupid people, which I am trying my best to douse whenever I can in a desperate attempt to feel like the wider impact of collective stupidity might be lessened even to the slightest extent. I’d be quite happy for others to perceive this attempt as pathetic - as I said, my “ego” doesn’t give a shit what you think of me, - but the problem is that stupid people tend to confuse “pathetic” with being as worthless as stupid. Only non-stupid people recognise that it doesn’t matter who is delivering an argument, so it shouldn’t matter that it’s an officially tested and confirmed fact that statistically I’m almost always the smartest guy in the room, but this doesn’t guarantee that stupid people are able to recognise this. In fact, the more people there are who are stupider than you maximises the number of people who are relatively too stupid to understand this fact - not least due to cognitive biases and poor education. This takes its toll over time - there’s a reason why I’ve singled you out to be impatient with. If you had eyes, you’d notice I’m being perfectly patient with EVERYONE else. This is even if they disagree with me. This is why you’re stupid for thinking I’m an impatient and uncooperative person in general, when this is highly exceptional behaviour on my part. Obviously none of this explanation will mean anything to you, because even though it’s the correct explanation, you are locked into ignoring correct explanations in favour of the first prejudicial assumption that came to your mind that best feeds your cognitive biases.
To quickly sweep up the above mess of a quote, as I have already repeatedly pointed out, quantities can refer to either the general abstract notion of “quantity” or a specific concrete instance of “a quantity”. “Number”, as a representation of quantity, can refer to the shape of “a number” i.e. the symbol that communicates this representation (as well as a shapeless sound of a word, or the shapeless abstract notion of number).
Just to unravel your blanket equivocation that “all numbers are shapeless”…
And yes, this is all factual and true, unlike “all horses are numbers”, which is contingent upon a drastic shift away from convention, and only to the extent of representation rather than direct identity.
There’s just so much oversight and truncated thought processes in everything you say…
I can handle that just fine in somebody who doesn’t relentlessly present themselves as someone who is indisputably correct about a subject on which they know they lack expertise, and as though someone who does know the subject is plainly wrong in face of the first thing that pops into your head. I care far less when people are simply wrong, it’s HOW you (in particular) are wrong that makes all the difference here. Again - if you had eyes you’d have noticed it’s only you who is a problem out of all the other people who aren’t agreeing with mathematical fact.
My problem, which again you incorrectly identify so predictably in line with common cognitive biases, is that I understand your points too easily. They’re all the same things I already considered when initially coming to understand this topic. To you it’s all advanced, insightful stuff, but if you weren’t stupid you would at least be able to comprehend in the abstract that this isn’t the same for everyone. And again this isn’t my ego, clearly I don’t care about what you think of me or I wouldn’t be such an asshole to you, and in front of everyone else. I care that you’re stupidly spreading stupidity and stupidity is an epidemic problem with the world. I care that people aren’t too stupid to understand correct facts and that they don’t present their incorrectness as correct with such certainty and persistence. These facts that I care about aren’t “me” - I care what people think about facts (whoever is sharing them) and their approach to talking about them - nothing more.
Yes, as I said, that’s what a “given” is. It’s not what a truth is. You can posit falsity as a given for the sake of valid argument. It just won’t be sound argument.
It’s not a fact that a horse is a number even if you posit it as a given. Stop equivocating.
It should be quite obvious that for (f(x)=0), (f(x)) represents the number (0). It also represents a function - more specifically the “way” (a doing) to get to the number (a being) that it already represents. Depending on the number in the set with which there is this binary relation - as in your copy/paste from Wikipedia - the function might represent a different number, but it represents a number regardless.
I really don’t see any point in continuing this, you’re not going to get it, nor ask questions if you don’t agree, which you won’t.