What is the difference between undefined and does not exist

In this case as x approaches zero from the right the values of the function seem to get close to every number between -1 and 1 on the y-axis. Again, in this situation, the limit does not exist. Go to Math Central. Quandaries and Queries. My name is Nicolasa, a current student and the level of this question is secondary When is the limit of f x undefined?

How would you divide it into no parts? It's undefined. You tend to see " does not exist " when you encounter imaginary numbers in the context of real numbers, or perhaps when taking a limit at a point where you get a two-sided divergence, such as:.

This would be due to the fact that a limit does not exist when the limit from both the positive and negative direction differ it's like trying to make two north poles of magnets meet, and when they meet, if they meet, that is their limitbut they never meet. In those cases, either the limit from one side exists only, or the domain of the function does not contain the desired limit.

Infinity is something that exists for us to quantify something that can never be truly reached in the absolute sense. Infinity is just an arbitrarily large number that we attribute to solutions that we know will keep increasing or decreasing forever. For example sqrt does not exist within RR. A value may not exist because different approaches to determining its value give different results. A value may not exist because a solution for the value is logically impossible. Jim H. An analogy: I can tell you what a unicorn, or a bigfoot is.

The jabberwocky is not defined, and it also does not exist. Infinity is used in different ways in different contexts in and outside of mathematics. Related questions How do I determine the molecular shape of a molecule? What is the lewis structure for co2? What is the lewis structure for hcn? Ignore the third question, it was worded incorrectly. Dec 23, 3, It depends on what exactly is meant by "expression" and what is meant by "simplify".

Feb 0. It is because the first one is undefined at 0, the second one is defined at 0. Multiplying both side by 5 is an equivalent step, multiplying by 0 is not an equivalent step. Dividing by 1 million is an equivalent step, dividing by zero is not equivalent step even not a step. So you can add -x to both side, it is an equivalent step for all x.

But you can't multiply or divide by x, because x is unknown yet. So we found one solution in this branch.