4

Is there a difference between non-existence and undefined?I'm confused. If there is a difference, when should we say it is not defined and when should we say it does not exist? For example

$\lim_{x\to 0}{\sqrt{x}}$ is undefined or non-existence?

or

Slope of vertical lines on the axis of $x$ is undefined or non-existence?

or

$\dfrac{1}{0}$ is undefined or non-existence?

Thank you for your guidance.

I apologize for my poor English writing.

311411
  • 3,537
  • 9
  • 19
  • 36
user1019364
  • 73
  • The phrasing "does not exist" is often used in the context of limits, whereas "undefined" is used otherwise. I would say that this is just a quirk of language rather than a mathematical issue, but perhaps others would disagree. – Joe Mar 27 '22 at 17:32
  • related discussions: https://math.stackexchange.com/questions/773652, https://math.stackexchange.com/questions/1228586, https://math.stackexchange.com/questions/1635691 – 311411 Mar 27 '22 at 17:44
  • Good question. One thing that comes to my mind, the square root of a negative number, in the Real domain does not exist, but in theory it can be defined I would say (from the definition of square root of a number you deduce it does not exist). And indeed it is then defined in the Complex domain where it does exist at that point...I am not sure it is just language ambiguity or there is a real distinction in term of philosophical meaning... – Marco Bellocchi Mar 27 '22 at 21:54

0 Answers0