But maths has defined a number that behaves non-numerically... we can at least agree that such ‘numbers’ are not to be used in the physical sciences?

These properties are nonsensical compared to the properties of any normal number.

X+1=X

No other number, complex, vector, matrix, whatever, has this nonsensical property.

Therefore transfinite cardinals are numbers — MindForged

Well transfinite cardinals have strange properties like:
X+1=X
X-1=X
What sort of number behaves like this?

Universe is not under obligation" to come up with a concept of time for it's own use — Victoria Nova

Don’t forget the speed of light - the universe has a built-in speed limit and speed = distance / time. A speed limit is needed for consistency of any universe. Hence time is a fundamental concept of this universe.

Sorry I meant I’ll-defined concept.

‘Aleph-null is defined as the first transfinite cardinal number and is the cardinality of the infinite set of the natural numbers’.

This definition is self contradictory; the cardinality of the natural numbers is not a number as it claims.

Add one to the cardinality of the natural numbers. — MindForged

I can’t because cardinality is an ill-defined concept - it includes cardinality of actually infinite sets - which are not numbers so I can’t add one to it.

Cardinality should be defined as the NUMBER of elements in a set. Actual infinity is not a NUMBER.

#1 is false because there are lots of infinities, with some being larger and smaller relative to others. — MindForged

- Yes but my argument shows none of them exist because they are not constructable

Adding one member to an infinite set does not increase its cardinality — MindForged

- So you are saying there is a number (cardinality) with the property that number plus one equals same number? X+1=X !!!

https://en.wikipedia.org/wiki/Galileo's_paradox

There are less squares than numbers because not all numbers are squares. Yet each number has a square so the number of numbers and squares must be the same.

He is trying to compare two actually infinite sets, IE comparing two undefined things. A set definition is not complete until all its members are interated.

- Actual Infinity is larger than any other number
- Actual infinity plus one is larger than actual infinity
- Hence there is no number larger than all other numbers
- Actual Infinity does not exist

Discribing the set is not the same as the set itself. The description is incomplete unless all members are iterated.

A set is an abstract object. It's criteria. Don't think of it in spacial terms — frank

The selection criteria for the set (for example the set of yellow cars) is different from the actual set (ie a number of distinct yellow cars). The later contains more information for example.

The definition of a set from Wikipedia starts with:

‘In mathematics, a set is a collection of distinct objects, considered as an object in its own right.’

The set of natural numbers is not constructable through any known operation hence it does not exist as a completed set.

Look someone made an error in set theory with the axiom of infinity and a lot of complex math has built up due to the complexities introduced by the logic error.

But the cardinality of the set of natural numbers will.never reach zero just by subtracting members — MindForged

You can’t take one from from Undefined

But my point is actual infinity is not a number so Actual Infinity is undefined in mathematics (except in set theory which merely declares that it exists as an axiom).

There is no natural number with the property that you can keep subtracting one from and never reach zero. Hence actual infinity does not exist.

bringing Zeno up so much makes it seem like there's no standard resolution to most of Zeno's paradoxes, which is just ignoring the calculus. — MindForged

- Calculus resolves Zeno’s paradoxes in a complex way.
- Denying Absolute Infinity (and thus implying discrete time) solves them in a simple way
- it also solves the other paradoxes of infinity (https://en.m.wikipedia.org/wiki/Paradoxes_of_infinity)
- Occams Razor simple solutions are better than complex ones.

Time is a construct created how? — frank

That’s a tricky question. If I had to construct time, I’d do it virtually using a computer simulation (think ‘The Sims’ - the game contains space and time but not our space and time and it’s created space and time). That is the basis of the simulation hypothesis (https://en.wikipedia.org/wiki/Simulation_hypothesis).

Well continuous time leads to paradoxes like Zeno’s. Archiles never catches the hair with continuous time because that requires Archiles to traverse an infinite number of steps. With discrete time there are no paradoxes, so we can eliminate continuous time I think.

But where did this base reality come from? — frank

It did not come from anywhere. It has permanent existence outside of time. Never created it just is. Time is a created construct that lives within this permanent base reality. The past present and future are all real. This is the view from Relativity.

So you are going even further than limiting infinity in physics and just denying the coherence of standard mathematics. — MindForged

I’m not saying maths is incoherent, just pointing out it’s impossible to define the cardinality of an infinite set so maybe infinite set is a flawed concept as was argued earlier...

The base reality has a beginning point? — frank

Thanks appreciate it! I’d imagine base reality has finite spacial dimensions so in a sense it would have beginnings and ends.

No it has a start and and end. Imagine all of finite space time as a static block that exists permanently. It’s the block universe view of Eternalism
https://en.wikipedia.org/wiki/Eternalism_(philosophy_of_time)

The Big Bang suggests a start of time. For something to exist it must have a start. A more elaborate argument for the start of time:

- Something can’t come from nothing
- So base reality must have always existed
- If base reality is permanent it must be timeless (proof: assume base reality existed forever within time - the total number of particle collisions would be infinite - reductio ad absurdum)
- So base reality must be timeless (to avoid the infinities) and permanent
- Time was created and exists within this permanent, timeless, base reality
- So time must be real, permanent and finite

I think they like to complicate things. Actual Infinity (a logical contradiction) is great for complicating things.

Once you rule out Actual Infinity, time has a start and quite a few models go out of the window. Infinity is keeping people in a job.

No I just believe in cause and effect.

Well i am a determinist but I don’t quite see what you mean?

Problem is the cosmologists are using the actually infinite. Eternal Inflation and the measure problem is an well known paradox.

I’m not a mathematician but the foundations of calculus are somewhat shaky as far as I can tell. Relies on an axiomatic definition of actual infinity from set theory IE thin air.

Actual Infinity
=
Cardinality of the set of natural numbers
=
Nonsense

But that does not mean that it is impossible for an infinite number of events to take place within a bounded period of time — Magnus Anderson

That would mean a physical system passing through an infinite number of states in a finite period of time. That’s spiritualism. That leads to Zeno’s paradoxes - absurdities. To avoid the absurdities time must be discrete.

And an infinite number of operations is impossible in the real world and impossible mathematically

Ok good point I overreached there. A different proof that Actual Infinity cannot exist mathematically:

- Actual Infinity is greater than any number
- But we can only make a number larger through addition or multiplication
- So there is no way to arrive at Actual Infinity.

Actual infinity cannot exist geometrically as there is no way to construct a line segment longer than all other line segments.

If you are a materialistic, you have to acknowledge Actual Infinity is impossible.

Yes, but a different number so I still assert:

- Actual infinity plus one equals Actual infinity
- but X+1 <> X for all X
- So Actual Infinity is absurd

But the concept of something that you add something to and it remains the same is nonsensical

When you add something to a number you get a different, larger number

More than Two Things plus one equals More than Two Things — Magnus Anderson

No it does not. X+1<>X

2nd proof that Actual Infinity does not exist:

- Actual infinity plus one equals Actual infinity
- but X+1 <> X for all X
- So Actual Infinity is absurd

Exactly my point Actual Infinity is a concept but it does not exist in reality.

All the paradoxes of infinity (https://en.m.wikipedia.org/wiki/Paradoxes_of_infinity) result from us having a logical facalcy (Actual Infinity) at the core of our reasoning.

The Actually Infinite has no place in the material world.