Sentence examples for an element of itself from inspiring English sources

Nothing seemed to preclude the possibility that some sets were elements of themselves while others were not, but, asked Russell, "What then of the set of all sets that were not elements of themselves?" If it is an element of itself, then it is not (an element of itself), but, if it is not, then it is.

But now what about the concept extension which is not an element of itself?

But E maps e to The True if and only if e is an extension which is not an element of itself, i.e., if and only if e is not an element of itself.

Let E represent this concept and let e name the extension of E. Is e an element of itself?

The extension of the concept spoon is not an element of itself, because that concept would map its own extension to The False (since extensions aren't spoons).

We have thus reasoned that e is an element of itself if and only if it is not, showing the incoherency in Frege's conception of an extension.

In logical terms, we are not allowed to quantify over a given class X when defining an element of X itself.

In D4, the introductory symmetry group, the left cosets gR of the subgroup R consisting of the rotations are either equal to R, if g is an element of R itself, or otherwise equal to (highlighted in green).

The weapon may be used to act out mock combat during the dance, or may be incorporated as an element of the dance itself, intertwining with other swords.

In 16 of these 24 states, lack of disclosure is an element of the crime itself, placing the burden of proof on the prosecution.

Such an index cannot, for instance, differentiate between different aspects of condition, such as fat deposition and muscle size, and it has been shown that such an index can retain an element of body size itself.