Metaphysics questions about infinity

[Leonid 0]

[...] That was not Ayn Rand's view. She considered it a useful concept of method. [...]

What is the method that Ayn Rand was referring to?

The method is the process of continually adding more.

There is no such a thing as an infinite number. That would mean a number without quantity, nothing in particular. That is why the laws of mathematics prohibit dividing by zero since A/0=inf. As result of such an operation every number would be equal to any other number and maths would become meaningless.

[Carlos 0]

[...] That was not Ayn Rand's view. She considered it a useful concept of method. [...]

What is the method that Ayn Rand was referring to?

The method is the process of continually adding more.

There is no such a thing as an infinite number.

As a concept of method in Mathematics, yes there is. When students integrate from -infinity to +infinity in order to determine the electrostatic field from an infinitely long, infinitely thin, cylinder of charge, they aren't successively describing reality by referencing concepts which don't exist or are invalid.

That would mean a number without quantity, nothing in particular.

Metaphysically there is never an infinite amount of something.

That is why the laws of mathematics prohibit dividing by zero since A/0=inf. As result of such an operation every number would be equal to any other number and maths would become meaningless.

A quantity divided by zero is undefined not because infinity doesn't exist, but because the process is literally undefined. To be divided means to be divided by a certain quantity; A/B means "how many groups of B are in A?" How many groups of zero are in A isn't definable, it's undefined.

[ewv 0]

[...] That was not Ayn Rand's view. She considered it a useful concept of method. [...]

What is the method that Ayn Rand was referring to?

The method is the process of continually adding more.

There is no such a thing as an infinite number.

As a concept of method in Mathematics, yes there is. When students integrate from -infinity to +infinity in order to determine the electrostatic field from an infinitely long, infinitely thin, cylinder of charge, they aren't successively describing reality by referencing concepts which don't exist or are invalid.

That does not make infinity a number.

That would mean a number without quantity, nothing in particular.

Metaphysically there is never an infinite amount of something.

That is why the laws of mathematics prohibit dividing by zero since A/0=inf. As result of such an operation every number would be equal to any other number and maths would become meaningless.

A quantity divided by zero is undefined not because infinity doesn't exist, but because the process is literally undefined. To be divided means to be divided by a certain quantity; A/B means "how many groups of B are in A?" How many groups of zero are in A isn't definable, it's undefined.

It is undefined in arithmetic, as operations on numbers. The meaning of infinity in this example and in the limits on integrals, as illustrated above, is in terms of limit processes employing higher level abstractions.

[Leonid 0]

[...] That was not Ayn Rand's view. She considered it a useful concept of method. [...]

What is the method that Ayn Rand was referring to?

The method is the process of continually adding more.

There is no such a thing as an infinite number.

As a concept of method in Mathematics, yes there is. When students integrate from -infinity to +infinity in order to determine the electrostatic field from an infinitely long, infinitely thin, cylinder of charge, they aren't successively describing reality by referencing concepts which don't exist or are invalid.

That would mean a number without quantity, nothing in particular.

Metaphysically there is never an infinite amount of something.

That is why the laws of mathematics prohibit dividing by zero since A/0=inf. As result of such an operation every number would be equal to any other number and maths would become meaningless.

A quantity divided by zero is undefined not because infinity doesn't exist, but because the process is literally undefined. To be divided means to be divided by a certain quantity; A/B means "how many groups of B are in A?" How many groups of zero are in A isn't definable, it's undefined.

That's right. Since the result of such an operation is undefined, infinity is undefined in actual terms, but it could be defined in potential terms. This is what a process of mathematical integration is all about-the expression of potentiality in actual terms.

[ewv 0]

That's right. Since the result of such an operation is undefined, infinity is undefined in actual terms, but it could be defined in potential terms. This is what a process of mathematical integration is all about-the expression of potentiality in actual terms.

What do you mean by that terminology? What are "actual terms" versus "potential terms", and if "actual terms" are required to "express" "potentiality" how can infinity be "defined in potential terms"? Integration is the inverse of the operation of differentiation and, in accordance with the fundamental theorem of calculus, simultaneously a summation. Why do you say it is "all about" the "expression of potentiality in actual terms"?