H - Many thanks for a really helpful post! Maybe what I'm exploring is to do with the boundary between mathematical formalism and realism. I'm now a little more clear about one or two things and I'll shut up about this now.
Btw - re the primes - I'll stop bothering you about this also. I've...
Hurkyl? Anybody? I'm getting a little bit paranoid at the lack of response. Was that not an appropriate question here? I suppose it's not exactly a mathematical question. Or is it? It wasn't a trap anyway. I was trying to understand how mathematicians see these issues, exactly where they feel...
Thanks. (I was careful to add 'in the everyday sense' when I used these words.)
That's how I imagine points are usually defined, as the end point of a never ending process. I assume that they simply have to be defined in this sort of way. It's the issues this raises that interest me.
Very...
Hurkyl - I think I can accept what you say (and I do) without it altering my general point, which comes exactly from trying to understand what parts of the object really do correspond to the math and what parts are simply errors of approximation. For most objects there may be no problem being...
Yes. Is it not a surreal fantasy about infinitely thin knives that produces a useable definition for infinitely 'thin' numbers? Whether such numbers exist (or whether numbers can be coherently defined in this way), I was suggesting, can be determined from examining the definition.
I suppose...
Okay CRG, I've decided to book some tuition in order to get to grips with the issues and will stop bothering you. I need to take a few steps back before trying to go forward again. Many thanks for your patience. Much appreciated.
Regards
Pete
Thanks - even if it's all hieroglyphics to me. I realise it's a struggle to talk about this with a mathematical duffer. I was wondering whether proving the zeros behave in a certain way is equivalent to proving that the relevant inputs have certain properties. But even if this question is...
Yes. Simplifying problems is a hobby. It works for the TPC, Russell's paradox and many other problems, (and it kept my business alive through many a crisis). I was wondering if it would work for RH. Seems highly unlikely at this point.
CRG - For you the point about inputs and outputs may not...
I like to think I could understand a lot of the maths, yes, given time, but I know I could never understand all that would be required for this problem. I'm in complete awe of anyone who can understand it.
I suppose I was asking if the zeta function is a map between inputs and outputs, such...
Thanks. I realise Goedel diagonalization is standard stuff. Couldn't understand the equations, which are also probably standard stuff.
The last point seems slightly off-track since I don't want to prove that zeta has certain properties. My thought was that zeta merely reveals properties...
Forgetting the OP then, I'd like to ask something about this.
I see that a region may be well-defined, so that being a region would not necessarily entail that a number is ill-defined. (Is this what you meant?) But... couldn't we say it is ill-defined when we forget that it's is a region and...
I can't follow most of this, but is there not a sense in which all numbers are ill-defined in the sense that they represent a region on the number line that can never be reduced to a point? In this way could the OP's question be something to do with the relationship between a continuum and a...
Hello everybody. It's my first post and I'm not a mathematician so please bear with me. I'll try to make it vaguely interesting.
I'm fascinated by the problem of deciding the Riemann Hypothesis. The trouble is, I'm not clever enough to understand it. The zeta function may as well be martian...