Zero division revisited

alan1000 August 20, 2024 at 14:44 1450 views 4 comments
A recent post asked:

What does it mean to divide by zero? In mathematics, this operation is undefined.

Back up the wagon, Chester! We first need to clarify: in which number line?

In the natural and relational number lines, the two integer lines we are mostly familiar with, "undefined" is probably the correct answer. I say "probably" because the history of mathematics is littered with the corpses of "undefinables" which subsequently proved to be definable.

In the hyperreal number line, it's wrong. In this line, 0 is one of the possible values of h, which is defined as a number which, for all values of n, is greater than -n and less than n. From this it follows that any number divided by 0 equals infinity, because 0 is a non-finite value equal to every other value within h. And thereby the calculus is made respectable.

Comments (4)

Lionino August 20, 2024 at 14:56 #926866
I am starting to convince myself that this user is a bot from 2014 reposting the same threads every 2 months.
alan1000 August 20, 2024 at 15:10 #926870
You could be right. And he's still waiting for answers.
T Clark August 20, 2024 at 16:19 #926877
Quoting alan1000
In the hyperreal number line, it's wrong.


It's not wrong, it's inapplicable.
Michael August 20, 2024 at 16:22 #926878
Quoting alan1000
In the hyperreal number line, it's wrong. In this line, 0 is one of the possible values of h, which is defined as a number which, for all values of n, is greater than -n and less than n. From this it follows that any number divided by 0 equals infinity, because 0 is a non-finite value equal to every other value within h. And thereby the calculus is made respectable.


No.

See division by zero:

In the hyperreal numbers, division by zero is still impossible.