Is infinity more than 6000?

[threaded]

It prevents mathematics from falling apart at the edges. Otherwise, no, not really.

I don't think it is required at the 'edges' either. As there aren't any really. It's much like the statement in a theory 'it can be seen', I'm like, maybe not...

[NotAllThere]

Since transfinite calculus was invented, there's been division among mathematicians about whether it's a good way of doing things. There's a group who reject the notion of infinite for reasons given here already. Mathematically, it's a valid position.

In my mind though, it's a limiting position. (excuse the pun, for those with the wit to spot it). Mathematics isn't about - how is this applicable? How does this help us understanding the real world? It is a simply an observation and investigation about how certain rules (axioms) fit together, and consequences of those axioms. When physics comes across something new, they generally find that the maths has already been invented - this was the case for relativity, quantum mechanics.

Mathematics already has areas of severe "edge". The whole issue of computability. "Will the rules of arithmetic ever lead to contradiction." Probably not - but it is has been proved that you can't prove that arithmetic will never lead to a contradiction.

The concept of infinity does have important, real world, implications. For example - it is provable to say "You can't design an algorithm to check whether a program is bug free".

Infinity is a very useful concept when you need to consider "all". In the above example, "all" computer programs. It turns out that the number of programs that can be written is the same as the number of real numbers that can be written out. So it turns out that understanding that the cardinality of the real numbers is "bigger" than that of the integers has important, real world implications.

Infinites are used in quantum mechanical calculations. Without these, we wouldn't have computers, lasers,... any digital consumer electronics.

Hey - but don't let that stop you whiffling on a subject where you haven't even the bare bones of understanding. This is CuK

[threaded]

I much prefer the 'good guess' to 'transfinite' theory.

If Physicists had followed Cantors continuum hypothesis we wouldn't have Quantum mechanics for example.

There again I follow the 'Copenhagen model' of quantum mechanics, (well I would ), and that the mathematics used is just a tool in the box that has been found to fit, rather than an actual 'good' description.