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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.

# Algebra Common Misconceptions: Level 1 Challenges

$\large \sqrt{4} = \, \color{red}{?}$

$\LARGE 2^{2^{2^{2^0}}} = \ ?$

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

Which of these numbers above is larger?

$\large \text{Is } 0.9999 \ldots = 1?$

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

$\large (a-b) - c = a - (b - c)$

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

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