Trivia

The <T> T[] toArray(T[]) Method of List

• The argument is used to specify the type of the template function(T) and store the results if possible(i.e. the size of the array is no smaller than the number of elements of the list).
• If the size of the array is no smaller than the size of the list, the first list.size() elements of the array become those in the list, while the remaining elements are left unchanged. In this case, the return value is the same as the argument.
• If the size of the array is smaller, then a new array will be allocated, assigned and returned. The array passed as the argument is left unchanged. In this case, the return value if NOT the same as the argument.
• The elements of the array are references to the same objects as those of the list.

See this sample code for further details.

Number of Prime Factors
$latex \forall n \le 10^{18}, \textrm{ the number of distinct prime factors of } n \le 15$

LaTeX Fonts and Emphasizing Control Sequences
Control sequences for changing fonts will be in effect until you change to other fonts explicitly, while emphasizing only affects the next character or group.

\bf{Bold both inside} and outside \rm
{\bf Bold only inside} but not outside
\emph{Ephasizing a few words} but not afterwards
{\emph Ephasizing only the first character} but not afterwards

Also pay attention that textbf, which is NOT font changing control sequences, plays the same role as emph.
There is no need to do italic correction in commands textit and textsl.

Spaces and Line Breaks in LaTeX
If you don't want a line break to act as a space, put a %(comment) at the end of this line.
If your sentence ends with an upper case letter, use "\@.".
~(tilde) represents a space not to be enlarged and make the parts separated by this space act as one word, i.e. line breaks are prohibited. Sometimes, "\ " or proper additional grouping is more appropriate, i.e. "\TeX\ is a typesetting program..." or "\TeX{} is a typesetting program...".

Dimension
The dimension of a geometric object is defined as the logarithm in base 2 of the number of copies of itself when each edge is magnified by a factor of 2. So the Sierpinski Sieve has dimension $latex \log_{2}3$.