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87 lines
3.8 KiB
HTML
87 lines
3.8 KiB
HTML
<div class="book-prose">
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<p>
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Mathematics begins with a simple question: <strong>how many?</strong> The smallest answers are
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<strong>0</strong> and <strong>1</strong>. Before you count birds, cups, or billions, you need to
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be sure you can tell <strong>nothing</strong> from <strong>one</strong>.
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</p>
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<h2 id="zero" class="book-prose__heading">Zero — nothing</h2>
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<p>
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When there is <strong>nothing</strong> to point at, we write <strong>0</strong> and say
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<strong>zero</strong>. An empty tray, a switched-off light with no glow, silence — no dot to
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count:
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</p>
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<p class="counting-dots counting-dots--empty" aria-label="zero dots">
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<span class="counting-dots__none">(none)</span>
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</p>
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<p>
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Zero is not “forgot to look.” It means <strong>none here</strong> — the answer when the amount
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is nothing.
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</p>
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<h2 id="one" class="book-prose__heading">One — exactly one</h2>
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<p>
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When there is a single thing to point at once, we write <strong>1</strong> and say
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<strong>one</strong>. One apple on the plate, one tap, one dot:
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</p>
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<p class="counting-dots" role="img" aria-label="one dot">
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<span class="counting-dots__dot"></span>
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</p>
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<p>One is not “a few” and not “many.” It is <strong>exactly one</strong>.</p>
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<h2 id="compare" class="book-prose__heading">Tell them apart</h2>
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<p>0 and 1 sit side by side. Mixing them up changes the whole answer.</p>
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<div class="zero-one-compare" role="group" aria-label="Zero compared with one">
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<div class="zero-one-compare__cell zero-one-compare__cell--zero">
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<p class="zero-one-compare__digit">0</p>
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<p class="zero-one-compare__word">zero</p>
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<p class="counting-dots counting-dots--empty" aria-hidden="true">
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<span class="counting-dots__none">none</span>
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</p>
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<p class="zero-one-compare__hint">nothing to count</p>
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</div>
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<div class="zero-one-compare__cell zero-one-compare__cell--one">
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<p class="zero-one-compare__digit">1</p>
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<p class="zero-one-compare__word">one</p>
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<p class="counting-dots" aria-hidden="true">
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<span class="counting-dots__dot"></span>
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</p>
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<p class="zero-one-compare__hint">one thing to count</p>
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</div>
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</div>
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<h2 id="true-and-false" class="book-prose__heading">True and false</h2>
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<p>
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You can also ask whether a <strong>statement</strong> matches the world. “The cup is on the
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table.” — if it is there, the statement is <strong>true</strong>. If the cup is not there, the
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statement is <strong>false</strong>.
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</p>
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<p>
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For a single yes-or-no question about <strong>one</strong> thing, the same care applies:
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</p>
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<ul>
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<li><strong>False</strong> fits when the answer is <strong>no</strong> — none of what we named, like <strong>0</strong>.</li>
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<li><strong>True</strong> fits when the answer is <strong>yes, exactly once</strong> — like <strong>1</strong> when we mean one clear match.</li>
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</ul>
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<p>
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Later you will meet longer counts and trickier logic. The habit starts here: look carefully, then
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decide — is it <strong>0 or 1</strong>? <strong>false or true</strong>?
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</p>
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<div class="book-callout" role="note">
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<p class="book-callout__label">The essence</p>
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<p>
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Telling <strong>0</strong> from <strong>1</strong> is the same kind of attention as telling
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<strong>false</strong> from <strong>true</strong>. That distinction is the foundation for every
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number and for understanding claims about the world.
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</p>
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</div>
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<div class="math-widget-mount" data-widget="zero-one-board" data-pagefind-ignore></div>
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<p>
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When you are steady with 0 and 1, continue to
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<a href="/math/counting-and-numbers/">Counting and numbers</a> to count past one and meet larger
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amounts.
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</p>
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</div>
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