For the Partial Function $f : \mathbf { Z } \times \mathbf { Z } \rightarrow \mathbf { R }$

question 115

Essay

For the partial function $f : \mathbf { Z } \times \mathbf { Z } \rightarrow \mathbf { R }$ defined by $f ( m , n ) = \frac { 1 } { n ^ { 2 } - m ^ { 2 } }$ , determine its domain, codomain, domain of definition, and set of values for which it is undefined or whether it is a total function.

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Definitions:

Number Conservation

The understanding that the quantity of a set of items is unchanged even when its appearance is altered, a concept developed in childhood.

Discrete Items

Individually separate and distinct elements or entities, often used in the context of data points or inventory.

Cognitive Tasks

Activities or exercises designed to assess or improve mental processes such as memory, reasoning, and problem-solving.