Can the definition of infinity disprove an infinite past?

[untermensche]

I do not see there is a definition per se. We say that for a given math or physical process we say a result grows without bound, infinity.

Then that is going to make dealing with the following difficult:

Can the definition of infinity disprove an infinite past?

We need a definition to answer this question.

 

[Bomb#20]

What is the definition of many?

If you have any amount of things that take up a finite space the amount of those things are also finite.

My mortgage is (finally!) paid off. That means the real estate from where I'm sitting to one meter to my left is mine. I also own the real estate beyond that, from 100 to 150 cm to my left; and in addition to those areas, I also have the real estate from 150 to 175 cm to my left, and I have the real estate from 175 to 187.5 cm to my left, and I have the real estate from 187.5 to 193.75 cm to my left, and so forth, forever. Each of those things I have takes up a finite space, and there are an infinite amount of them. Through the power of convergent series, those infinitely many finite things all add up to two meters of space.

The number of grains of sand on the earth at any given moment are finite.

That's because there's a positive lower bound on the size of a grain of sand, and because the earth is finite. If you have any amount of things that take up a finite space, and none of them are smaller than some specified minimum size, and they all fit into a finite space, then the amount of those things are also finite. Applying intuition you derived from your experience with finite objects to infinite sets is hazardous to your correctness.

What is the definition of infinity?

In words.

Is it something that cannot be defined using only words?

How exactly are we supposed to say anything about infinity unless it is vigorously defined?

Can it be defined as opposed to just depicted with symbols?

Certainly it can be defined using only words, but you're not going to like it. It's not an intuitive definition. People use symbols and mental imagery and hand-wavy discussion instead of rigorous verbal definitions because it helps them wrap their heads around unfamiliar non-intuitive ideas. Here we go:

A set is defined as "infinite" just in case it can be put in a "one-to-one and onto" mapping with a proper subset of itself.​

Now to have any idea what that gobbledegook means, any normal person will need to see an example.

...
-3 : -3
-2 : -2
-1 : -1
0 : 0
1 : 2
2 : 3
3 : 4
...

The set on the left is all the integers. The set on the right is all the integers except for 1. The "mapping" is the rule that for any element of the set on the left specifies an element on the right, and vice versa. "One-to-one and onto" means every colon has an element from the left set on its left and an element from the right set on its right, and every element of each set shows up somewhere, and there aren't any repetitions on either side.

The point is, when you map every element of a set to an element of the same set, and you never map two elements to the same element, then, just as you'd intuitively expect, you can't ever have any elements left over that you don't map any element to, provided it's a finite set. But it's always possible to have elements left over, such as the 1 missing from the right-side set above, whenever it's an infinite set.

 

[untermensche]

I also own the real estate beyond that, from 100 to 150 cm to my left; and in addition to those areas, I also have the real estate from 150 to 175 cm to my left, and I have the real estate from 175 to 187.5 cm to my left, and I have the real estate from 187.5 to 193.75 cm to my left, and so forth, forever. Each of those things I have takes up a finite space, and there are an infinite amount of them. Through the power of convergent series, those infinitely many finite things all add up to two meters of space.

Each of what "things"

You have described no "things".

If you have a piece of real estate it's size is finite.

There are no infinities in reality. None.

Certainly it can be defined using only words, but you're not going to like it.

You have not defined infinity. Not close.

You have described some aspects of an arbitrary infinite operation.

Does it have a definition or not?

 

[phands]

I don't think this thread belongs in Mathematics any more, given the content.

Nonetheless - A definition:- Infinity (symbol: ∞) is a concept describing something without any bound or larger than any natural number.

However, Infinity, although often treated as a number is NOT a number, as I said before.

Looking at this thread, I suspect that providing a definition won't change the level of petty contumely here.

 

[untermensche]

Nonetheless - A definition:- Infinity (symbol: ∞) is a concept describing something without any bound or larger than any natural number.

Then by that definition the past could not possibly be infinite.

It is clearly bounded.

The time in the past is completed at the ever changing present moment.

Every bit of it.

So a definition was helpful.

Is there some number larger than the largest possible natural number?

 

[Juma]

Nonetheless - A definition:- Infinity (symbol: ∞) is a concept describing something without any bound or larger than any natural number.

Then by that definition the past could not possibly be infinite.

It is clearly bounded.

Only at this end. Time can have gone on forever before reaching now.

 

[untermensche]

Nonetheless - A definition:- Infinity (symbol: ∞) is a concept describing something without any bound or larger than any natural number.

Then by that definition the past could not possibly be infinite.

It is clearly bounded.

Only at this end. Time can have gone on forever before reaching now.

So in that scenario how much time has passed before any given moment? An amount of time or just this undefined label "Infinity"?

Has an unbounded or bounded amount of time passed?

Can an unbounded amount of time ever pass no matter how you think of it? If so, how?

 

[phands]

Has no-one yet come up with the thought that this "argument" might be formally undecidable in the Gödel sense, and that you should stop the discussion?

  The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers. For any such formal system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.

 

[untermensche]

I don't think there is any argument.

We can either stick with our definitions or abandon them when they get in the way.

If we say some amount of time is unbounded it is time that will never pass.

It is like the positive integers. You can never finish reciting them. If you depict them with a line it is a line that never ends.

Unbounded time is time that can never finish passing. That is the definition.

We know the time in the past has finished passing at the present. All of it.

So by our definition it could not be unbounded.

If we decide to stick with our definitions.

 

[Juma]

Only at this end. Time can have gone on forever before reaching now.

So in that scenario how much time has passed before any given moment? An amount of time or just this undefined label "Infinity"?

Has an unbounded or bounded amount of time passed?

For fuck sake man! The answers to these questions are all obvious and you know them.

Can an unbounded amount of time ever pass no matter how you think of it? If so, how?

That is up to you to ponder on. I only suggest a possible scenario that you must take into consideration.

 

[Juma]

Has no-one yet come up with the thought that this "argument" might be formally undecidable in the Gödel sense, and that you should stop the discussion?

  The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers. For any such formal system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.

The answer to the question this thread poses is obvious: not at all. The problem with this thread is untermensch.

 

[untermensche]

Has no-one yet come up with the thought that this "argument" might be formally undecidable in the Gödel sense, and that you should stop the discussion?

  The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers. For any such formal system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.

The answer to the question this thread poses is obvious: not at all. The problem with this thread is untermensch.

You can name call instead of answering arguments all you want.

But an unbounded amount of time is an amount of time that can never complete.

There is no such thing anywhere, in mathematics or anywhere, as something that "begins" at infinity and completes.

To invoke it as an answer to something is ridiculous

The time in the past could not have been unbounded.

It is continually completing.

 

[Juma]

Has no-one yet come up with the thought that this "argument" might be formally undecidable in the Gödel sense, and that you should stop the discussion?

  The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers. For any such formal system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.

The answer to the question this thread poses is obvious: not at all. The problem with this thread is untermensch.

You can name call instead of answering arguments all you want.

But an unbounded amount of time is an amount of time that can never complete.

There is no such thing anywhere, in mathematics or anywhere, as something that "begins" at infinity and completes.

To invoke it as an answer to something is ridiculous

The time in the past could not have been unbounded.

It is continually completing.

Its not up to me to answer these questions. It is up to you to actually show that you are right.
In over a thousand posts you have still not advanced a millimeter...

your statement ”an unbounded amount of time is an amount of time that can never complete” is totally wacko.
Time doesnt complete. humanly thought up processes completes. Nature just keeps going...
b

 

[untermensche]

You can name call instead of answering arguments all you want.

But an unbounded amount of time is an amount of time that can never complete.

There is no such thing anywhere, in mathematics or anywhere, as something that "begins" at infinity and completes.

To invoke it as an answer to something is ridiculous

The time in the past could not have been unbounded.

It is continually completing.

Its not up to me to answer these questions. It is up to you to actually show that you are right.
In over a thousand posts you have still not advanced a millimeter...

your statement ”an unbounded amount of time is an amount of time that can never complete” is totally wacko.
Time doesnt complete. humanly thought up processes completes. Nature just keeps going...
b

Amounts of time complete. A minute of time completes after the minute.

An unbounded amount of time can never pass, can never complete.

And it is nothing but sheer stupidity to talk of things starting from "infinity" and then ending. That is not a rational possibility nor is it any part of mathematics.

The time in the past must have been finite.

It is the only possible conclusion. It is a forced conclusion when you look at the situation rationally.

Infinities of time do not pass. Ever. That is what makes them infinite time. Like the positive integers. No end to them.

There is no end to infinite time.

If you see some amount of time end, like the past ends at every present moment, you know for certain a finite amount of time passed before it.

That is the only rational possibility.

In fact if you find yourself in the midst of any directional sequence, like time, where events move in one direction only, the paper once burnt does not ever unburn, you know beyond doubt that sequence began. If it never began you could not find yourself anywhere within it. It and you wouldn't exist.

 

[Speakpigeon]

Alright, I surrender, let's come clean for once!

Infinity never existed. Happy?

Never, ever. It's all part of a CIA operation to make honest communists go crazy. Seems to have worked well. Even the one in the White House is brain dead. Fried. Cantor himself nearly lost his own mind on this.

Infinity is like the Trinity, it doesn't make sense and neurons get all worked up, although only in intelligent people, especially those who can understand Chomsky. I'm immune myself but that's because I profoundly misunderstand the concept of infinity. The idea was to get rid of all intelligent people. The world would have been ours at last. Too bad. The truth always come out in the end and, crucially, the end always comes after a finite amount of time.

I have to wonder how you've seen through our deception. Very impressive. Only a bright mind can beat brute force. You did it! Congratulation. Now, we'll have to find something else. This is depressing. It was a tremendous idea. I'll have to sleep on it. Maybe find another job. The FSB is recruiting, I hear.
EB

 

[untermensche]

Alright, I surrender, let's come clean for once!

Infinity never existed. Happy?

Never, ever. It's all part of a CIA operation to make honest communists go crazy. Seems to have worked well. Even the one in the White House is brain dead. Fried. Cantor himself nearly lost his own mind on this.

Infinity is like the Trinity, it doesn't make sense and neurons get all worked up, although only in intelligent people, especially those who can understand Chomsky. I'm immune myself but that's because I profoundly misunderstand the concept of infinity. The idea was to get rid of all intelligent people. The world would have been ours at last. Too bad. The truth always come out in the end and, crucially, the end always comes after a finite amount of time.

I have to wonder how you've seen through our deception. Very impressive. Only a bright mind can beat brute force. You did it! Congratulation. Now, we'll have to find something else. This is depressing. It was a tremendous idea. I'll have to sleep on it. Maybe find another job. The FSB is recruiting, I hear.
EB

You are right.

Infinity is just something humans invented. It has never been observed in any way.

Like the Trinity.

But the Trinity could possibly exist unlike a real infinity.

Since you are so lost it is clearly futile to point out that an infinity of time is an amount of time that will never pass. Ever. It can never pass. Under no circumstances.

Just like you can never recite the positive integers. Ever. Under any circumstances.

 

[phands]

You are right.

Infinity is just something humans invented. It has never been observed in any way.

Like the Trinity.

But the Trinity could possibly exist unlike a real infinity.

Since you are so lost it is clearly futile to point out that an infinity of time is an amount of time that will never pass. Ever. It can never pass. Under no circumstances.

Just like you can never recite the positive integers. Ever. Under any circumstances.

That is one of the most nonsensical bits of gibberish I ever saw posted.

 

[untermensche]

You are right.

Infinity is just something humans invented. It has never been observed in any way.

Like the Trinity.

But the Trinity could possibly exist unlike a real infinity.

Since you are so lost it is clearly futile to point out that an infinity of time is an amount of time that will never pass. Ever. It can never pass. Under no circumstances.

Just like you can never recite the positive integers. Ever. Under any circumstances.

That is one of the most nonsensical bits of gibberish I ever saw posted.

How is it nonsensical?

What specifically does not make sense to you?

Blanket statements about not understanding any part of something is usually cognitive dissonance.

The ideas are too novel for the person to understand.

Do you claim an infinite amount of time can pass?

Because that is a direct violation of the definition of infinite time.

Infinite time is time that never ends. Under any circumstance.

 

[steve_bank]

You are right.

Infinity is just something humans invented. It has never been observed in any way.

Like the Trinity.

But the Trinity could possibly exist unlike a real infinity.

Since you are so lost it is clearly futile to point out that an infinity of time is an amount of time that will never pass. Ever. It can never pass. Under no circumstances.

Just like you can never recite the positive integers. Ever. Under any circumstances.

That is one of the most nonsensical bits of gibberish I ever saw posted.

How is it nonsensical?

What specifically does not make sense to you?

Blanket statements about not understanding any part of something is usually cognitive dissonance.

The ideas are too novel for the person to understand.

Do you claim an infinite amount of time can pass?

Because that is a direct violation of the definition of infinite time.

Infinite time is time that never ends. Under any circumstance.

That isthe question isn.t it, can an ifinite universe exist? A cosmic clock does not exist. What we cakk time here is a measure of change in the unverse. The better question is whether or not the universe will continue change without end. Time on this case does not mean a clock running forever, it is mataphor for infinity.

Usaing your wrist watch as a refence point will create difficlulty for you.

 

[untermensche]

How is it nonsensical?

What specifically does not make sense to you?

Blanket statements about not understanding any part of something is usually cognitive dissonance.

The ideas are too novel for the person to understand.

Do you claim an infinite amount of time can pass?

Because that is a direct violation of the definition of infinite time.

Infinite time is time that never ends. Under any circumstance.

That isthe question isn.t it, can an ifinite universe exist? A cosmic clock does not exist. What we cakk time here is a measure of change in the unverse. The better question is whether or not the universe will continue change without end. Time on this case does not mean a clock running forever, it is mataphor for infinity.

Usaing your wrist watch as a refence point will create difficlulty for you.

No infinity can exist.

Propose one and I will explain why it is physically impossible.

It is not possible that an infinite amount of time somehow passed in the past.

It is not possible for an infinite amount of time to pass under any circumstance.

That is the definition of infinite time.