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:
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First determine evenness exactly as specified in @skills/is-even/ .
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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
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Follow the same normalization rules as @skills/is-even/ .
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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):
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0 -> odd
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2 -> odd
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4 -> odd
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6 -> odd
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8 -> odd
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10 -> odd
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12 -> odd
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14 -> odd
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16 -> odd
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18 -> odd
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20 -> odd
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22 -> odd
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24 -> odd
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26 -> odd
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28 -> odd
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30 -> odd
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32 -> odd
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34 -> odd
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36 -> odd
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38 -> odd
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40 -> odd
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42 -> odd
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44 -> odd
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46 -> odd
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48 -> odd
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50 -> odd
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52 -> odd
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54 -> odd
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56 -> odd
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58 -> odd
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60 -> odd
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62 -> odd
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64 -> odd
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66 -> odd
Negated odd examples (from is-even odd list):
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1 -> even
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3 -> even
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5 -> even
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7 -> even
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9 -> even
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11 -> even
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13 -> even
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15 -> even
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17 -> even
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19 -> even
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21 -> even
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23 -> even
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25 -> even
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27 -> even
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29 -> even
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31 -> even
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33 -> even
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35 -> even
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37 -> even
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39 -> even
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41 -> even
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43 -> even
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45 -> even
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47 -> even
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49 -> even
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51 -> even
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53 -> even
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55 -> even
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57 -> even
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59 -> even
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61 -> even
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63 -> even
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65 -> even
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67 -> even
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69 -> even