Is Odd
Purpose
Explain and determine oddness as the logical negation of evenness, using the same variable names: n, remainder, is_even, is_odd.
Relationship to Is Even
Oddness is defined as the negation of evenness for integers:
- First determine evenness exactly as specified in
@skills/is-even/. - Then negate that result:
is_odd =!is_even.
In other words, a number is odd if and only if it is not even. This definition is complete and exhaustive for integers: every integer is either even or odd, never both.
Determining Oddness Template
Use this structure when responding:
Input: <value>
Normalized integer (n): <integer or "not an integer">
Calculation: remainder = n % 2
Decision: is_even = (remainder == 0)
Negation: is_odd = !is_even
Result: <odd|even|not applicable>
Rationale: <short explanation>Normalization Notes
- Follow the same normalization rules as
@skills/is-even/. - For non-integers, odd/even is not applicable unless rounding is requested.
Example Set (derived from is-even examples)
All examples below are the @skills/is-even/ examples with the result negated.
Negated even examples (from is-even even list):
- 0 -> odd
- 2 -> odd
- 4 -> odd
- 6 -> odd
- 8 -> odd
- 10 -> odd
- 12 -> odd
- 14 -> odd
- 16 -> odd
- 18 -> odd
- 20 -> odd
- 22 -> odd
- 24 -> odd
- 26 -> odd
- 28 -> odd
- 30 -> odd
- 32 -> odd
- 34 -> odd
- 36 -> odd
- 38 -> odd
- 40 -> odd
- 42 -> odd
- 44 -> odd
- 46 -> odd
- 48 -> odd
- 50 -> odd
- 52 -> odd
- 54 -> odd
- 56 -> odd
- 58 -> odd
- 60 -> odd
- 62 -> odd
- 64 -> odd
- 66 -> odd
Negated odd examples (from is-even odd list):
- 1 -> even
- 3 -> even
- 5 -> even
- 7 -> even
- 9 -> even
- 11 -> even
- 13 -> even
- 15 -> even
- 17 -> even
- 19 -> even
- 21 -> even
- 23 -> even
- 25 -> even
- 27 -> even
- 29 -> even
- 31 -> even
- 33 -> even
- 35 -> even
- 37 -> even
- 39 -> even
- 41 -> even
- 43 -> even
- 45 -> even
- 47 -> even
- 49 -> even
- 51 -> even
- 53 -> even
- 55 -> even
- 57 -> even
- 59 -> even
- 61 -> even
- 63 -> even
- 65 -> even
- 67 -> even
- 69 -> even