RX-wiki

P-ness

The “p-ness” of r ∈ ℚ is defined as |n| / (s - |n| + 1), where s is the sum of all absolute exponents in the canonical form of |r|, and p^n is the corresponding term in such canonical form (n=0 if the term isn’t present).

Examples

• the 2-ness (AKA “even-ness”) of ±2 is 1, because 2=2^1 and 1/1 = 1
• 2-ness of ±3 is 0
• 2-ness of ±1/2 is 1
• 2-ness of ±18 is 1/3, because 18 = 2^1 ⋅ 3^2 and 1/(3-1+1) = 1/3

• 2-ness of ±4/3 is 1, because 4/3 = 2^2 ⋅ 3^-1 and 2/(2+

  -1

  -2 +1) = 1

• 3-ness of ±192 is 1/7, because 192 = 2^6 ⋅ 3^1 and 1/(6+1) = 1/7

Name

“p-ness” has similar pronunciation to “penis” in english, and (coincidentally) “penes” in español. This was unintentional, but now it’s intentional, because “funi”