x in X
question: What is in X?, context: A function f from X to Y is a subset of the Cartesian product X × Y subject to the following condition: every element of X is the first component of one and only one ordered pair in the subset. In other words, for every x in X there is exactly one element y such that the ordered pair (x, y) is contained in the subset defining the function f. This formal definition is a precise rendition of the idea that to each x is associated an element y of Y, namely the uniquely specified element y with the property just mentioned.
What is in X?
In other words, for every x in X there is exactly one element y such that the ordered pair (x, y) is contained in the subset defining the function f.
A function f from X to Y is a subset of the Cartesian product X × Y subject to the following condition: every element of X is the first component of one and only one ordered pair in the subset. In other words, for every x in X there is exactly one element y such that the ordered pair (x, y) is contained in the subset defining the function f. This formal definition is a precise rendition of the idea that to each x is associated an element y of Y, namely the uniquely specified element y with the property just mentioned.
In other words, for every <hl> x in X <hl> there is exactly one element y such that the ordered pair (x, y) is contained in the subset defining the function f.
A function f from X to Y is a subset of the Cartesian product X × Y subject to the following condition: every element of X is the first component of one and only one ordered pair in the subset. In other words, for every <hl> x in X <hl> there is exactly one element y such that the ordered pair (x, y) is contained in the subset defining the function f. This formal definition is a precise rendition of the idea that to each x is associated an element y of Y, namely the uniquely specified element y with the property just mentioned.
A function f from X to Y is a subset of the Cartesian product X × Y subject to the following condition: every element of X is the first component of one and only one ordered pair in the subset. <hl> In other words, for every x in X there is exactly one element y such that the ordered pair (x, y) is contained in the subset defining the function f. <hl> This formal definition is a precise rendition of the idea that to each x is associated an element y of Y, namely the uniquely specified element y with the property just mentioned.