# Tagged Questions

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### Why is an image called an “image”?

Given a function $f : A \to B$, the image, denoted by $\operatorname{Im}f$ is the set of all $f(x)$ where $x \in A$. Why do we call this set the image? When was it first used, and what motivated its ...
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### Understanding the difference between relations and functions.

$R=\{(1,2),(1,3)\}$ is a relation but not function. The logic for this is that if the first element of every ordered pair must remain different, then it is said to be function. Otherwise, it's just ...
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### Concept of a function and Idea of a formula as a function; History of

Enderton Elements of Set Theory, p. 43 (1977, Academic Press), writes: There was a reluctance to separate the concept of a function itself from the idea of a written formula defining the function. ...
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### Terminology Regarding Basic Properties of Functions

Is there a cultural difference between saying that a function is 1-to-1 or injective, onto or surjective and a 1-to-1 correspondence or bijective?
### The origin of the function $f(x)$ notation
What are the historical origins of the $f(x)$ notation used for functions? That is when did people start to use this notation instead of just thinking in terms of two different variables one being ...