# Total

This crossword clue is for the definition: Total.
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Last seen on: LA Times Crossword 15 Jun 2018, Friday

### Random information on the term “Total”:

In mathematics, a partial function from X to Y (written as f: X ↛ Y or f: X ⇸ Y) is a function f: X ′ → Y, for some subset X ′ of X. It generalizes the concept of a function f: X → Y by not forcing f to map every element of X to an element of Y (only some subset X ′ of X). If X ′ = X, then f is called a total function and is equivalent to a function. Partial functions are often used when the exact domain, X, is not known (e.g. many functions in computability theory[example needed]).

Specifically, we will say that for any x ∈ X, either:

For example, we can consider the square root function restricted to the integers

Thus g(n) is only defined for n that are perfect squares (i.e., 0, 1, 4, 9, 16, …). So, g(25) = 5, but g(26) is undefined.

There are two distinct meanings in current mathematical usage for the notion of the domain of a partial function. Most mathematicians, including recursion theorists, use the term “domain of f” for the set of all values x such that f(x) is defined (X’ above). But some, particularly category theorists, consider the domain of a partial function f:X → Y to be X, and refer to X’ as the domain of definition. Similarly, the term range can refer to either the codomain or the image of a function.

### Random information on the term “REAL”:

Reality is all of physical existence, as opposed to that which is merely imaginary. It is the name for all of physical existence, but the word is also used in a declension to speak of parts of reality that include the cognitive idea of an individual “reality” (i.e. psychology), to a “situational reality,” or a “fictional reality.”

The term is also used to refer to the ontological status of things, indicating their existence, but this is simply the idea of giving names to smaller “realities,” and seems vague and academic without the idea of physical existence as the first “reality,” and the others being smaller parts.

Philosophical questions about the nature of reality or existence or being are considered under the rubric of ontology, which is a major branch of metaphysics in the Western philosophical tradition. Ontological questions also feature in diverse branches of philosophy, including the philosophy of science, philosophy of religion, philosophy of mathematics, and philosophical logic. These include questions about whether only physical objects are real (i.e., Physicalism), whether reality is fundamentally immaterial (e.g., Idealism), whether hypothetical unobservable entities posited by scientific theories exist, whether God exists, whether numbers and other abstract objects exist, and whether possible worlds exist.