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authorMarshall Lochbaum <mwlochbaum@gmail.com>2020-07-18 23:17:04 -0400
committerMarshall Lochbaum <mwlochbaum@gmail.com>2020-07-18 23:18:10 -0400
commitc63290ae05990f54619207ac6ee0b3fbf6f9c145 (patch)
tree12951802a4190e69ae7edda9ed84fe4df735bca5 /docs/doc/logic.html
parent6243dcd88bf70157d600e787a7c344541df98085 (diff)
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<h2 id="examples">Examples</h2>
<p>We can form truth tables including the non-integer value one-half:</p>
<pre> <span class='Function'>¬</span> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>0.5</span><span class='Ligature'>‿</span><span class='Number'>1</span>
-<span class='Value'>[</span> <span class='Number'>1</span> <span class='Number'>0.5</span> <span class='Number'>0</span> <span class='Value'>]</span>
+1‿0.5‿0
<span class='Function'>∧</span><span class='Modifier'>⌜˜</span> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>0.5</span><span class='Ligature'>‿</span><span class='Number'>1</span>
-<span class='Value'>┌</span>
- <span class='Number'>0</span> <span class='Number'>0</span> <span class='Number'>0</span>
- <span class='Number'>0</span> <span class='Number'>0.25</span> <span class='Number'>0.5</span>
- <span class='Number'>0</span> <span class='Number'>0.5</span> <span class='Number'>1</span>
- <span class='Value'>┘</span>
+0 0 0
+0 0.25 0.5
+0 0.5 1
<span class='Function'>∨</span><span class='Modifier'>⌜˜</span> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>0.5</span><span class='Ligature'>‿</span><span class='Number'>1</span>
-<span class='Value'>┌</span>
- <span class='Number'>0</span> <span class='Number'>0.5</span> <span class='Number'>1</span>
- <span class='Number'>0.5</span> <span class='Number'>0.75</span> <span class='Number'>1</span>
- <span class='Number'>1</span> <span class='Number'>1</span> <span class='Number'>1</span>
- <span class='Value'>┘</span>
+ 0 0.5 1
+0.5 0.75 1
+ 1 1 1
</pre>
<p>As with logical And and Or, any value and 0 is 0, while any value or 1 is 1. The other boolean values give the identity elements for the two functions: 1 and any value gives that value, as does 0 or the value.</p>
<h2 id="why-not-gcd-and-lcm-">Why not GCD and LCM?</h2>