Scientific results here and now apply to there and then

Strathos · Nov 4, 2019

Just chiming in to say that transfinite numbers are a real thing in mathematics. It's not some left-wing plot just because it has 'trans' in the name.

Sam91 · Nov 4, 2019

Strathos said:
Just chiming in to say that transfinite numbers are a real thing in mathematics. It's not some left-wing plot just because it has 'trans' in the name.

Now, if you had put the word that included 'finite' in bold I would have rated it a winning post.

klutedavid · Nov 4, 2019

sjastro said:
Answer the question.
If infinite sets do not exist then show us how you can sum the finite set {0.3, 0.03, 0.003, 0.0003…………} to obtain 0.33333 recurring.

The same way that you add elements in a finite set. The answer is still always a finite answer and that is guaranteed and no matter how many finite additions you perform.

You can't count using finite numbers and reach an infinite number, no matter how long you want to count finite numbers for.

klutedavid · Nov 4, 2019

Strathos said:
Just chiming in to say that transfinite numbers are a real thing in mathematics. It's not some left-wing plot just because it has 'trans' in the name.

An infinite number does not exist. In fact, the infinite cannot be measured or quantified.

klutedavid · Nov 4, 2019

Sam91 said:
From a philosophical stance one could possibly state that once you have expressed N you have bounded it, even though it does not yet have a value. You see which ever number it is, it will be only one specific integer. Thus it is finite. It will be no more, no less and will just be. N+1 will be one integer more than the value assigned to N

It shall probably only exist for a finite time... the record and memory of it shall pass away. If 'immortalised' in a very enduring substance, it will still probably not endure indefinitely. Lol

It seems quite definite to me

That's correct.

Let N be any natural number.

All N values only ever inhabit a set with a cardinal value that is a natural number. To say otherwise is to distort the initial definition of N.

essentialsaltes · Nov 4, 2019

klutedavid said:
Since no element of the set of positive integers can be anything other than a positive integer, the onus is on you to specify. The specific element of that positive integer set that is not a finite member.

What is the cardinality of this unique set that you mentioned?

sjastro · Nov 4, 2019

klutedavid said:
The same way that you add elements in a finite set. The answer is still always a finite answer and that is guaranteed and no matter how many finite additions you perform.

You can't count using finite numbers and reach an infinite number, no matter how long you want to count finite numbers for.

I asked for an answer not a deflection.

Sam91 · Nov 4, 2019

Really? That's cool! lol. There was me just trying to join in the fun.

klutedavid · Nov 4, 2019

essentialsaltes said:
What is the cardinality of this unique set that you mentioned?

The cardinality of any set of positive integers will always be a natural number. Do you have difficulty with what I just said.

There can never be an infinite set of positive integers as positive integers are finite numbers.

Count positive integers for an extended period and you will always only ever have, a cardinal value that is a natural number. There is no twilight zone in mathematics.

To even hint that while counting the elements (i.e., positive integers) of a set you will reach an undefined, non natural number. Is simply not true.

Sam91 · Nov 4, 2019

klutedavid said:
The cardinality of any set of positive integers will always be a natural number. Do you have difficulty with what I just said.

There can never be an infinite set of positive integers as positive integers are finite numbers.

Count positive integers for an extended period and you will always only ever have, a cardinal value that is a natural number. There is no twilight zone in mathematics.

To even hint that while counting the elements (i.e., positive integers) of a set you will reach an undefined, non natural number. Is simply not true.

I agree.

Even if one keeps counting until they died, they still would not have uttered an infinite integer.

Infinity is a construct, it doesn't exist. Even a loop is not infinite because all other directions are bounded. It is a concept for lazy folk who have no perseverence

.

klutedavid · Nov 4, 2019

sjastro said:
I asked for an answer not a deflection.

That is not a deflection.

Any set with a cardinal value of an infinite value is undefined, you must declare the value of the term 'infinite'.

1 divided by ∞, is not a mathematical operation because ∞ is undefined in any numerical sense.

klutedavid · Nov 4, 2019

Sam91 said:
I agree.

Even if one keeps counting until they died, they still would not have uttered an infinite integer.

Infinity is a construct, it doesn't exist. Even a loop is not infinite because all other directions are bounded. It is a concept for lazy folk who have no perseverence .

Your on the ball.

Integers can never be anything but integers.

Sets of integers are only sets of integers.

The number of elements of any set of integers is always a natural number.

No matter how big a set of integers one could ever imagine, the cardinal value is always a natural number.

Infinite sets do not exist because the cardinal value of an infinite set is not a natural number.

Sam91 · Nov 4, 2019

klutedavid said:
Your on the ball.

Integers can never be anything but integers.

Sets of integers are only sets of integers.

The number of elements of any set of integers is always a natural number.

No matter how big a set of integers one could ever imagine, the cardinal value is always a natural number.

Infinite sets do not exist because the cardinal value of an infinite set is not a natural number.

I'm not sure what the Cardinals have to do with mathematics though.

essentialsaltes · Nov 4, 2019

klutedavid said:
The cardinality of any set is always a natural number.

You have mentioned a number of specific sets. What is the cardinality of any of these that you have talked about?

klutedavid said:
Integers are finite numbers and the set of all positive integers are bounded within that set of finite numbers.

klutedavid said:
Consider the set of positive integers, {1,2,3,...}

klutedavid said:
The set of all numbers (Z) cannot be defined as an infinite set, as the set (Z) can never approach an infinite point. Because that point or number is not defined in mathematics.

klutedavid said:
The set of natural numbers starts at zero and has a bound. An infinite set is unbounded.

The set of integers are divided into positive and negative integers, both positive and negative integers are bounded at zero.

klutedavid said:
Since no element of the set of positive integers can be anything other than a positive integer, the onus is on you to specify. The specific element of that positive integer set that is not a finite member.

Sam91 · Nov 4, 2019

klutedavid said:
That is not a deflection.

Any set with a cardinal value of an infinite value is undefined, you must declare the value of the term 'infinite'.

1 divided by ∞, is not a mathematical operation because ∞ is undefined in any numerical sense.

I agree.

In my opinion 1/0 should not be classed as undefined though. It should be classed either as impossible or 1. Personally I think the 0 should cancel out the divide and it should remain as 1. There is one cake, zero people need a slice of cake. There is still one cake... It must be bad cake if it is that unappealing. Maybe it shouldn't be defined as cake if nobody wants it. Most people like cake.

klutedavid · Nov 4, 2019

essentialsaltes said:
You have mentioned a number of specific sets. What is the cardinality of any of these that you have talked about?

Always a natural number of course.

klutedavid · Nov 4, 2019

Sam91 said:
I'm not sure what the Cardinals have to do with mathematics though.

The number of elements in a set is called the cardinal value of a set.

The set {1,2,3} has a cardinal value (size) of 3.

sjastro · Nov 4, 2019

klutedavid said:
That is not a deflection.

Any set with a cardinal value of an infinite value is undefined, you must declare the value of the term 'infinite'.

1 divided by ∞, is not a mathematical operation because ∞ is undefined in any numerical sense.

Not only is it a deflection but a capitulation.
Your failure to demonstrate how 0.33333 recurring can be expressed by adding a finite number of terms proves it.

46AND2 · Nov 4, 2019

klutedavid said:
Your on the ball.

Integers can never be anything but integers.

Sets of integers are only sets of integers.

The number of elements of any set of integers is always a natural number.

No matter how big a set of integers one could ever imagine, the cardinal value is always a natural number.

Infinite sets do not exist because the cardinal value of an infinite set is not a natural number.

By your rationale with all this, 1/3 is not a real number. Nor is pi, or e. You realize that, right?

Certainly big news for the math world.

You should let the world know. You'll be the next famous mathematician.

Tinker Grey · Nov 4, 2019

46AND2 said:
By your rationale with all this, 1/3 is not a real number. Nor is pi, or e.

Well, 1/3 can be as long as one is willing to change bases any time a repeater comes up. Transcendentals on the other hand ...

Scientific results here and now apply to there and then

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