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In mathematics, the term undefined is often used to refer to an expression which is not assigned an interpretation or a value (such as an indeterminate form, which has the possibility of assuming different values).
Broadly speaking, undefined means there is no possible value (or there are infinite possible values), while indeterminate means there is no value given the current information. For example in the equation ax + by = c, the relation between x and y is indeterminate because you can't determine it without knowing the values of a, b and c.
- 8 min
- Sal Khan
Apr 10, 2015 · Undefined means there does not exist an answer in the way we defined it. For example, if we define a function $f$ $|$ $\mathbb R \mapsto \mathbb R$ by $f(x) = 2x$, then $f(x)$ is "defined" for $x$ a real number. $x = 1$, $f(x) = 2$. $f(4) = 8$. However, $f(orange)$ makes no sense. It's undefined since orange is not an element of $\mathbb R$.
Sep 3, 2022 · The "first level" answer should be: "undefined" plainly means "not defined", i.e. the expression has no value. For example, $\frac{a}{0}$ is undefined for all $a\in\mathbb R$, $\tan(k\pi+\pi/2)$ is undefined for all $k\in\mathbb Z$, $\log(x)$ is undefined for $x\le 0$.
Why dividing by zero is undefined (video) | Khan Academy. Course: Algebra 1 > Unit 1. Math > Algebra 1 > Algebra foundations > Division by zero. Why dividing by zero is undefined. Google Classroom. About. Transcript. As much as we would like to have an answer for "what's 1 divided by 0?" it's sadly impossible to have an answer.
- 4 min
- Sal Khan
Dec 10, 2018 · Thanks. Sheryl knew three facts: 0 ÷ n = 0 for any number n. n ÷ 0 is undefined for any number n. n ÷ n = 1 for any number n. But 0 ÷ 0 fits all three rules, so what happens when math “rules” do battle? Is the result 0, or undefined, or 1? The answer turns out to be “undefined”, but there’s a lot to be considered.
In the case of rational expressions, we can input any value except for those that make the denominator equal to 0 (since division by 0 is undefined). In other words, the domain of a rational expression includes all real numbers except for those that make its denominator zero. Example: Finding the domain of x + 1 ( x − 3) ( x + 4)
