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# Common Misconceptions (Algebra)

Arm yourself with the tools to be the king or queen of heady mathematical debates, like the age old question of whether 0.999.... = 1.

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\[\large \sqrt{4} = \, \color{red}{?}\]

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Gabe Smith**

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\[ \LARGE 2^{2^{2^{2^0}}} = \ ? \]

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Amisha Gupta**

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\[\large A = \frac{1}{\left(\frac{0.5}{0.25}\right)} \hspace{5mm} \text{or} \hspace{5mm} B = \frac{\left(\frac{1}{0.5}\right)}{0.25}\]

Which of these numbers above is larger?

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Zandra Vinegar**

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\[\large \text{Is } 0.9999 \ldots = 1? \]

Note. The "\(\ldots\)" indicates that there are infinitely many 9's.

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Jake Lai**

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\[ \large (a-b) - c = a - (b - c)\]

Suppose \(a, b\) and \(c\) are numeric variables. Under what conditions is the equation above true?

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Damon Demas**

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