Mathcad Enhancement Proposal (MEP) - Extend the scope of ℤ to include all IEEE 754 consecutive integers, where ℤ is the set of integers.
Mathcad's Is-Element-Of operator x ∈ y determines whether x is an element of y, where y is one of the sets ℂ (complex numbers), ℝ (real numbers), ℚ (rational numbers), or ℤ (integers). Is-Element-Of works both symbolically and numerically (except ℚ in the latter's case).
When numerically evaluating x for membership in ℤ, x must lie between -231 and +231-1. However, Mathcad handles numbers as 64-bit IEEE 754 floating-point numbers; thus, the full range of consecutive numerical integers in Mathcad is -253 and +253-1.
The maximum positive floating point real number, realmax, is 1.7976931348623157×10308.
realmax ∈ ℝ and realmax + realmax×1i ∈ ℂ both return true (1).
Implementing this MEP would mean Mathcad gave the correct and consistent result for all (#) Mathcad IEEE 754 64-bit numbers when evaluated against the sets ℂ, ℝ, and ℤ.
(I've had to implement my own isinteger function to test numbers for membership in numerical ℤ to overcome this restriction)
Stuart
(#) ∞ (infinity) is the subject of another MEP. Numerical infinity should behave in a manner consistent with symbolic infinity.
