2 May 2018

One

\(1\) is the identity element for multiplication of real numbers.

\(1\) is not a prime number! By definition, a prime number has exactly two divisors: \(1\) and the number itself.

\(0!=1\), even as \(1!=1\).

\(\log_a a=1\), for all \(a \in \mathbb R\).

\(a^0=1\), for all \(a \in \mathbb R\backslash \{0\}\).

\(1\) is the measure of the radius of the unit circle and \(\sin^2x+\cos^2x=1\).

Note the results of the following multiplications:

\(1 \times 1 =1\).
\(11 \times 11=121\).
\(111 \times 111=12,321\).
\(1,111 \times 1,111=1,234,321\)
\( \cdots \)

They are all palindromic numbers, i.e., numbers that remains the same when its digits are reversed and which is attributed good luck.

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