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--- numeric [2025/02/27 21:06] – inverse, not xor. carl
+++ numeric [2026/03/14 21:01] (current) – carl
@@ Line 36: / Line 36: @@
 As a consequence of their representation, most operations on numeric types are not true to their eponymous  mathematical function.  For example, adding two Int32 numbers can overflow, resulting in a wrong answer.  Also, most floating point operations are not associative: (a + b) + c != a + (b + c).  This is usually uncommon enough that it isn't a problem, but care should be taken to programming defensively.
+===== Support in Languages =====
+==== Java ====
+Main: [[java:numeric|Java Numeric]].
+===== Numeric Observations =====
+When dividing two quantities, the quotient and the remainder have different units.   For example, 10 apples divided by 3 apples is 3, but the remainder is 1 apple.  Note that the quotient unit changed.
+The units may be different too.  Consider calculating the quotient and remainder of 10 meters in 3 seconds.
+A = 10 meters
+B = 3 seconds
+Q = floor(A / B)
+R = A % B
+This maintains the identity A = Q * B + R.  Thus:
+Q = 3 meters/second
+R = 1 meter
+===== Taylor Series =====
+The Taylor Series for the exponential function diverges quickly if less than 100 terms are used.  These terms tend to have enormous numerators and denominators.   The numerator is usually x^100, and the denominator is 100!.   Floating point math is not suited to represent these values as the number of terms exceeds 100ish.