• alan1000
    200
    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.
  • Lionino
    2.7k
    I am starting to convince myself that this user is a bot from 2014 reposting the same threads every 2 months.
  • alan1000
    200
    You could be right. And he's still waiting for answers.
  • T Clark
    13.7k
    In the hyperreal number line, it's wrong.alan1000

    It's not wrong, it's inapplicable.
  • Michael
    15.4k
    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.alan1000

    No.

    See division by zero:

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