Devans99

The result of that work from a century ago is the Dedekind-Cantor continuum - which is a nonsensical proposition. I'm not sure you read / understood t...

Name calling does not win arguments.

If space and time are creations then they must be finite and discrete (impossible to create anything infinitely big or small). But I feel a more direc...

A past infinity of time is an impossibility. For example: perpetual motion is impossible, we have motion, hence time must have a start. There are a se...

The Difference Between Actual and Potential Infinity Imagine the real numbers in the interval . Is there an actual or potential infinity of them? Well...

I understand what an integral is and the concept does not lead to a sound definition of a continuum - unless you can correct me on this?

Agreed. That numerical value does not tell us the width of a point and length is the sum of widths of the constituent points / sub-line segments.

I class myself as a realist but a finite realist, which I consider to be a more 'materialistically real' proposition than a realist who believes in ac...

But maybe God is omnipotent within the bounds of common sense / logic? So he can do anything logical but cannot for example, square a circle. One of t...

An axiom is a statement - statements are true or false. End of story. Treating aleph0 as a mathematical concept leads to paradoxes, eg: https://en.wik...

- He felt that something with zero extent like a point could not constitute something with non-zero extent, like a line. - He also regarded points on ...

Aristotle made a fuss about zero-dimensional points being the components of lines so I feel the question can be regarded as an open philosophical ques...

The normal definition of axiom: 'a statement or proposition which is regarded as being established, accepted, or self-evidently true.' The mathematica...

If all you've ever experienced is pleasure and you've never experienced pain then you place less value in pleasure than someone who has experienced pa...

The problem of evil is a real show stopper for theologians, they wrap themselves in terrible logical knots trying to circumvent it. The best I can thi...

I'm more interested in the nature of our reality and the nature of real lines rather than abstract/imaginary mathematical lines. IE is it possible for...

I suppose you can view a line segment as constituted of points or sub-segments. Whichever way though, the length of the constituents has to be non-zer...

Thanks for the links… Wrestled with - and consistently failed to achieve - a sound mathematical description of continua - as I also failed to in the O...

Try to focus on the current discussion - my OP - and give me some counter arguments. This is a philosophy forum, not a mud slinging contest.

As usual, character assassination but no counter arguments.

Just a definition. Sort of like defining ?=?. Meaningless IMO. Why?

My argument in the OP is that alpeh-zero must be finite. What problem(s) do you have with that argument?

See the argument given in this OP: https://thephilosophyforum.com/discussion/7309/whenhow-does-infinity-become-infinite/p1 IE induction leads to the c...

I agree with you, \sum_{n \to \infty} 1, tends towards but never attains a purely imaginary concept/state called infinity. (Actual) Infinity is not a ...

Thanks @"A Seagull"! This forum has many folk like @"tim wood" who accept the received 'wisdom' of Cantor and co without question - it is refreshing t...

My interest in maths stops when maths stops telling me about the nature of reality. Transfinite maths and reality are greatly in opposition. ?+1=? tel...

Does infinity have existence beyond our minds? All sorts of things like fairies, square circles, can exist in our minds but only a subset can take a c...

Thats not a counter argument.

OK give me an example of an actually infinite set from nature. Arithmetic is defined, actual infinity has no sound definition. So its fair game for th...

All your counter arguments have been countered so you resort to mud slinging. Just typical of you.

- Infinity does not exist - see the OP - so this whole conversation is about MARSH GAS - Even if infinity existed, finity is a subset of infinity and ...

Depends on the hardware/software you are using I guess. Computers use discrete binary representations of numbers. Computers are real. Reality is real....

As you can imagine I am not a believer in the possibility of continua occurring in nature and I am not alone in this belief (eg loop quantum gravity)....

Yes and the rules set theory defines are broken. If something goes on forever, you can't count it - even with an infinity of time it is not possible t...

There are only three possibilities. A number of the real number line must have: 1. A zero width 2. A non-zero width 3. A undefined width So how many r...

Numbers exist in our minds only so we can imagine a zero width number and an UNDEFINED number of numbers in a finite interval. If you were to try to r...

God be praised - a counter argument from @"Tim Wood" - a miracle! In each finite segment of the naturals, the number of naturals is approximately twic...

:grimace: You are full of s**t. If you had any counter arguments to my points you would post them... but you don't so shut up.

OK I get you: https://www.compoundchem.com/2016/03/22/boiling-point/

100 °C What is your point exactly?

This point in a slightly different guise, is discussed at length on another thread: https://thephilosophyforum.com/discussion/comment/362707 In short ...

This is known as Galileo paradox: https://en.wikipedia.org/wiki/Galileo%27s_paradox I share Galileo's rather than Cantor's opinion, but I am in the mi...

I think on step 6 above, saying 1*?=? is a circular definition so is not too enlightening. I think my doubts are around how infinity is defined. Limit...

I find the concept of a dimensionless object difficult - it has no extents so it cannot have any existence - how can any sound reasoning performed wit...

I find the notion that there are an actually infinite number of identical me/planet earth/this galaxy in time and/or space to be absurd, so I tend to ...

Art is a subclass/subtype of information? Then what is astronomy? Fields pervade the universe such as the Higgs field etc... these fields fluctuate in...

Sorry I should of said: - A point has zero length according to maths definition - But according to my intuition, a point must have non-zero length

I would contend that set theory gives an unwarranted legitimacy to actual infinity which influences the physical sciences. Some cosmologists are obses...

We are talking about the nature of time, whether it has a beginning or end specifically. Such a conversation is intimately linked to the existence or ...

"There are, however, contexts in which division by zero can be considered as defined. For example, division by zero z/0 for z in C^*!=0 in the extende...