As usual, we start with basic algebraic computation drilling at the beginning of F.4 mathematics lessons. But, I just did some useless mathematical chatting and gave something about infinity (e.g. the discussion of 1 – 1 + 1 – 1 + … ) and they showed their excitment with hands clapping. Well, of course, I switched to serious matter very soon. As expected, most of the students did not know the fact that “zero is an even number" (even, they did not know that zero is an integer). I went through some ‘prerequisite’ questions with them, one is:
(a) [True or false?]
(b) If , then . [True or false?]
(c) The square roots of 9 are 3 and -3. [True or false?]
(d) If , then and . [True or false?]
F.4 students, here are the answers.
Here are some explanations.
(a) The symbol represents “the positive square root of 9″. only, not .
(b) If , then or . We may also write “If , then “. It is because, both and satisfy the equation .
(c) To make it clear, we write:
The positive square root of 9 is 3. [In symbol, ]
The negative square root of 9 is -3. [In symbol, ]
The square roots of 9 are 3 and -3.
(d) We should write “If , then or ." On writing “ and “, it means, the value of is 3 and -3 at the same time, which is impossible. Also, you may read (c) again, we used the conjunction “and" there, it is possible because we are not talking about the single value of , but the “square roots of 9″, and there are 2 different values of “square roots of 9″, namely 3 and -3.
Minor thing added,
suppose and are roots of , then, can we say something like
“ or “?
It is not that OK to express the solution as above (why?), instead, you may write
and or and
(note: the above two ways involve set notations)