Write the missing number: note: write the numbers in such a way that the sum of two neighbouring numbers should be the same as the sum of the pair of the numbers at the opposite ends.â
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Answer:
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✔If we persist in retaining such errata in our educational texts, an unwitting or unscrupulous person could utilize the result to show that 1 = 2 as follows:
(a).(a) - a.a = a2 - a2
for any finite a. Now, factoring by a, and using the identity
(a2 - b2) = (a - b)(a + b) for the other side, this can be written as:
a(a-a) = (a-a)(a+a)
dividing both sides by (a-a) gives
a = 2a
now, dividing by a gives
1 = 2, Voila!
This result follows directly from the assumption that it is a legal operation to divide by zero because a - a = 0. If one divides 2 by zero even on a simple, inexpensive calculator, the display will indicate an error condition.
Again, I do emphasis, the question in this Section goes beyond the fallacy that 2/0 is infinity or not. It demonstrates that one should never divide by zero [here (a-a)]. If one does allow oneself dividing by zero, then one ends up in a hell. That is all.

If the result of dividing by zero (which is a meaningless operation in the first place) by calculator was infinity, then calculator would give you "infinity" not the word "error", or "E", this is so, because only a limited number of letters such as E or the word Error could be formed. Therefore, any illegal operation will default to the error indicator. The Error message means that "the operation you have performed is illegal, such as dividing by zero." Right? The calculator does the mathematical operations, but does not have a mind of its own. Your mind does the interpretation of the results.
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