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==Selection 10==
==Selection 10==
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===The Signs for Multiplication (cont.)===
{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
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<p>'''The Signs for Multiplication''' (cont.)<p>
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<p>The sum <math>x + x\!</math> generally denotes no logical term. But <math>x,_\infty + \, x,_\infty</math> may be considered as denoting some two <math>x\!</math>'s.</p>
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<p>The sum 'x' + 'x' generally denotes no logical term. But 'x',<sub>∞</sub> + 'x',<sub>∞</sub> may be considered as denoting some two 'x's.</p>
<p>It is natural to write:</p>
<p>It is natural to write:</p>
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: <p>'x' + 'x' = !2!.'x'</p>
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{| width="100%"
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| width="10%" |
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<p>and</p>
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| align="center" | <math>x + x ~=~ \mathit{2}.x</math>
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| width="10%" |
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: <p>'x',<sub>∞</sub> + 'x',<sub>∞</sub> = !2!.'x',<sub>∞</sub></p>
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|-
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| <p>and</p>
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| align="center" | <math>x,_\infty + \, x,_\infty ~=~ \mathit{2}.x,_\infty</math>
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<p>where the dot shows that this multiplication is invertible.</p>
<p>where the dot shows that this multiplication is invertible.</p>