The idea of an infinite past

[fast]

Whatever definition is meant when discussing things like natural numbers, whole numbers, integers, and rational numbers.

That's exactly what I'm trying to get you to clarify. Most people just rely on a vague implicit "I know it when I see it" definition for what counts as a 'number' that breaks down fairly quickly when scrutinized, especially when counter-intuitive concepts like infinity are considered.

Would you accept these Merriam-Webster definitions?

(1) : a unit belonging to an abstract mathematical system and subject to specified laws of succession, addition, and multiplication
(2) : an element (such as π) of any of many mathematical systems obtained by extension of or analogy with the natural number system

If so, then I don't see why infinity shouldn't be a number. Of course, it isn't a member of the standard number systems (naturals, integers, rationals, reals, complex, etc), so you may see people saying "Infinity is not a number" but that's an answer to a different question.

Ok, so infinity is a number.

Thanks.

 

[untermensche]

The concept that needs examination is not infinity.

It is a "completed infinity".

Something totally different.

And not just a completed infinity a "real completed infinity".

Something that apparently can appear whole by magic.

Can anybody actually demonstrate a real completed infinity is possible?

 

[Beer With Straw]

The concept that needs examination is not infinity.

It is a "completed infinity".

Something totally different.

And not just a completed infinity a "real completed infinity".

Something that apparently can appear whole by magic.

Can anybody actually demonstrate a real completed infinity is possible?

Wait! Wait!

 

[fast]

The concept that needs examination is not infinity.

It is a "completed infinity".

Something totally different.

And not just a completed infinity a "real completed infinity".

Something that apparently can appear whole by magic.

Can anybody actually demonstrate a real completed infinity is possible?

Does zooming far enough into an otherwise seemingly solid object and finding empty space proof positive of what you're saying?

 

[beero1000]

Wait! Wait!

Heh. I'm stealing that.

 

[untermensche]

You mention the concept of a "real completed infinity" and heads explode.

I await the proof a real completed infinity is possible.

Like I said apparently they appear whole.

Like the gods.

I take real completed infinities just as seriously.

 

[Beer With Straw]

You mention the concept of a "real completed infinity" and heads explode.

I await the proof a real completed infinity is possible.

Like I said apparently they appear whole.

Like the gods.

I take real completed infinities just as seriously.

Are you talking to me or someone else?

 

[untermensche]

You mention the concept of a "real completed infinity" and heads explode.

I await the proof a real completed infinity is possible.

Like I said apparently they appear whole.

Like the gods.

I take real completed infinities just as seriously.

Are you talking to me or someone else?

I am asking anyone who thinks a real completed infinity is possible how they acquired that knowledge.

There are no tricks that can be played with reality.

And no infinity can be assumed.

 

[Beer With Straw]

Well, isn't the observable universe thought of as a closed system, so there could a lot of what we don't understand that is not observed.

And maybe a better question might be has mathematics in history ever devolved into something more stupid?

As for now, for a real infinity, math says a clear: FUCK NO!

 

[Speakpigeon]

Well, who knows, maybe we could get to agree on a pragmatic solution to this difficult question of whether infinity is real or not.

So, obviously lots of people will use irrational numbers without much thinking about the metaphysical implications, but maybe we could help them.

So, first, what is an irrational number?

Here's a dictionary definition:

irrational number
(Mathematics) any real number that cannot be expressed as the ratio of two integers, such as π

That should be clear enough to all of us around here I guess.

Now, the example given here, π is also a transcendental number. What's that?

Here it is:

transcendental number
(Mathematics) an irrational number that is real but not algebraic, that is, one that is not a root of any polynomial expression with rational coefficients, such as π or e

That's a bit more technical but you all know more about this stuff than I do so it should be good enough.

We all understand how π is used in life but the question is, do we really need to see it as a transcendental number, or would it be enough to cut it down to size to a more ordinary perspective.

So, first, here's the definition of π:

π
2. (Mathematics) A transcendental number, approximately 3.14159, represented by the symbol π, that expresses the ratio of the circumference to the diameter of a circle and appears as a constant in many mathematical expressions.

So, it's made clear here that π is a very useful number. To cut it down to size, it's also very easy. We would just have to replace in the definition of π "approximately 3.14159" with "equal 3.14159", and just use this in our calculations.

Now, this should be considered as a pragmatic decision. No more metaphysical debate now. A "yes", or a "no"!

And, oops, sorry, also why, but only in terms of practical consequences of doing it or not doing it.
EB

 

[Beer With Straw]

Well, who knows, maybe we could get to agree on a pragmatic solution to this difficult question of whether infinity is real or not.

So, obviously lots of people will use irrational numbers without much thinking about the metaphysical implications, but maybe we could help them.

So, first, what is an irrational number?

Here's a dictionary definition:


That should be clear enough to all of us around here I guess.

Now, the example given here, π is also a transcendental number. What's that?

Here it is:


That's a bit more technical but you all know more about this stuff than I do so it should be good enough.

We all understand how π is used in life but the question is, do we really need to see it as a transcendental number, or would it be enough to cut it down to size to a more ordinary perspective.

So, first, here's the definition of π:

π
2. (Mathematics) A transcendental number, approximately 3.14159, represented by the symbol π, that expresses the ratio of the circumference to the diameter of a circle and appears as a constant in many mathematical expressions.

So, it's made clear here that π is a very useful number. To cut it down to size, it's also very easy. We would just have to replace in the definition of π "approximately 3.14159" with "equal 3.14159", and just use this in our calculations.

Now, this should be considered as a pragmatic decision. No more metaphysical debate now. A "yes", or a "no"!

And, oops, sorry, also why, but only in terms of practical consequences of doing it or not doing it.
EB

There is already precision and accuracy in calculations. You've not given the answer to circumference of a circle to two billion digits in math class when r is only denoted as say 5.

Are you thinking about Planck length or something?

 

[untermensche]

Well, isn't the observable universe thought of as a closed system, so there could a lot of what we don't understand that is not observed.

And maybe a better question might be has mathematics in history ever devolved into something more stupid?

As for now, for a real infinity, math says a clear: FUCK NO!

It's not a mathematical question. And it's more than a real infinity.

It's a real completed infinity.

It's a question about the nature of reality and the rational assumptions that can be made about reality.

It is irrational to assume any infinities are real or could be real.

 

[Beer With Straw]

Well, isn't the observable universe thought of as a closed system, so there could a lot of what we don't understand that is not observed.

And maybe a better question might be has mathematics in history ever devolved into something more stupid?

As for now, for a real infinity, math says a clear: FUCK NO!

It's not a mathematical question.

It's a question about the nature of reality.

Um... I'm pretty confident the universe has to do with the nature of reality in some way.

Maybe I'm thinking about something else, but yeah.

 

[untermensche]

Well, isn't the observable universe thought of as a closed system, so there could a lot of what we don't understand that is not observed.

And maybe a better question might be has mathematics in history ever devolved into something more stupid?

As for now, for a real infinity, math says a clear: FUCK NO!

It's not a mathematical question.

It's a question about the nature of reality.

Um... I'm pretty confident the universe has to do with the nature of reality in some way.

Maybe I'm thinking about something else, but yeah.

But the question as to whether a real completed infinity is possible is not a mathematics question.

No such thing exists in mathematics or could be proven using mathematics.

 

[Beer With Straw]

Um... I'm pretty confident the universe has to do with the nature of reality in some way.

Maybe I'm thinking about something else, but yeah.

But the question as to whether a real completed infinity is possible is not a mathematics question.

No such thing exists in mathematics or could be proven using mathematics.

Erm... Isn't mathematics the best language used to describe reality?

I'm kinda' lost here, but please don't hold it against me.

:EDIT:

OK, wait a second. I'm in a Metaphysics subforum, hence, I think I missed the point and didn't read the sign on the way in.




And yeah, I've also had a couple beers; I wanted to indulge.

 

[untermensche]

Um... I'm pretty confident the universe has to do with the nature of reality in some way.

Maybe I'm thinking about something else, but yeah.

But the question as to whether a real completed infinity is possible is not a mathematics question.

No such thing exists in mathematics or could be proven using mathematics.

Erm... Isn't mathematics the best language used to describe reality?

I'm kinda' lost here, but please don't hold it against me.

Mathematics is used as a part of models which are abstractions of reality. But no model is just mathematics.

And when the models can make predictions they are thought to approximate, not replicate, reality.

 

[Speakpigeon]

Erm... Isn't mathematics the best language used to describe reality?

I'm kinda' lost here, but please don't hold it against me.

Mathematics is used as a part of models which are abstractions of reality. But no model is just mathematics.

And when the models can make predictions they are thought to approximate, not replicate, reality.

Come on, try to beer with him!
EB

 

[Beer With Straw]

Erm... Isn't mathematics the best language used to describe reality?

I'm kinda' lost here, but please don't hold it against me.

Mathematics is used as a part of models which are abstractions of reality. But no model is just mathematics.

And when the models can make predictions they are thought to approximate, not replicate, reality.

Come on, try to beer with him!
EB

It'd be her BTW, but I was already tempted to post a Feynman quote: It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.


1+1=2 is not mathematical argument that has ever failed experiment. M-Theory has no technology available to be experimented on, yet is the best idea for unifying GR and QM.

:EDIT:

And quantum mechanics has never failed experiment and GR hasn't either.

 

[Kharakov]

Um... I'm pretty confident the universe has to do with the nature of reality in some way.

Maybe I'm thinking about something else, but yeah.

But the question as to whether a real completed infinity is possible is not a mathematics question.

No such thing exists in mathematics or could be proven using mathematics.

Erm... Isn't mathematics the best language used to describe reality?

I'm kinda' lost here, but please don't hold it against me.

:EDIT:

OK, wait a second. I'm in a Metaphysics subforum, hence, I think I missed the point and didn't read the sign on the way in.

I see you have meet untermensche. The person who designed them doesn't own up to it, in public. Needless to say, there is a method to their madness.


unterprime directive: If you can't be wrong right, be wrong wrong.

 

[untermensche]

Come on, try to beer with him!
EB

It'd be her BTW, but I was already tempted to post a Feynman quote: It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.


1+1=2 is not mathematical argument that has ever failed experiment. M-Theory has no technology available to be experimented on, yet is the best idea for unifying GR and QM.

:EDIT:

And quantum mechanics has never failed experiment and GR hasn't either.

Yes, the models are good enough to be of use.

That doesn't make reality connected to mathematics.

The models use mathematics.

And the models are abstractions of reality. Not a replication of reality.