Not true. Let's choose 'A' as the arbitrary symbol.
Then 1/0 = A.
Divide both sides by A and you get 1/0 = 1.
Divide both sides by 2A and you get 1/0 = 1/2.
. . .
You know, for a moment I thought you got me there. But then it occurred to me you are making a mistake (in my book anyway). Let me quote myself from another post:
The only problem remaining is to define 0/0 (or 0*G): is it 0, G, or a real number? That's the only problem I could find.
The reason you're getting nonsense is because you are defining 0/0, or A*0. I still think that is really the only problem. Can you prove me wrong?
Not very consistent. I'd say it's nonsense.
As far as I can tell, we can define x/0 for x 0 and remain consistent, so long as we do not define 0/0. But I'd love to hear a second opinion.
"It's ironic that people like Paul argue that math is completely abstract, and yet still think of "a very small number" as being entirely different from "zero"."
Sorry, I don't see the irony.
If math is completely abstract, then we can substitute every instance of the number '0' with, say, '&'. We can also replace any instance of "the smallest number you can think of" with, say, '#'.
Exactly what are the unique properties of '&', as compared to #, $, ^, !, or any other purely abstract symbol?
"Things"? Things supposed to exist? No mathematician talks about such "things"
They do, but they claim they don't. That's the irony.
The only things mathematicians talk about are concepts, not real things.
If mathematicians can't define 'real', how can they be sure they're not dealing with 'real' things? In other words, where is the formal proof that mathematics doesn't deal with real things?
I say this a matter of opinion, because I can't prove it, but mathematicians seem to say it's a matter of logic, even though they can't prove it. That's where I see the irony. I may be missing their point, but I don't see how.
But in any case, the mathematical concept of existence is completely different from, and unrelated to, the physical or ontological concept of existence.
If it's different, then it's not the same thing.
"Abstract thought is the shortest route to confusion."
Did you just make that up, or can you quote a reliable source?
I can answer that as soon as you explain to me why that information matters.
I think abstract thought is the only route to human success.
That is only true if you consider philosophy the only thing in which humans can be successful. I personally think philosophy is the only thing in which humans can't possibly be successful. So you can have an idea of the gulf in opinion between us. Which is good.