Binary number numerals. For example, the binary numeral 100 is pronounced "one zero zero", rather than "one hundred", to make its binary nature explicit, and for purposes of correctness. Since the binary numeral 100 represents the value four, it would be confusing to refer to the numeral as "one hundred" (a word that represents a completely different value, or amount). Alternatively, the binary numeral 100 can be read out as "four" (the correct "value"), but this does not make its binary nature explicit. Counting in binary is similar to counting in any other number system. Beginning with a single digit, counting proceeds
Combinatorial number system "C"<nowiki>'</nowiki>, since they have the same largest part 9, but the next largest part 6 of "C" is less than the next largest part 7 of "C"<nowiki>'</nowiki>; the sequences compared lexicographically are (9,6,4,3,0) and (9,7,3,1,0). Another way to describe this ordering is view combinations as describing the "k" raised bits in the binary representation of a number, so that "C" = {"c"...,"c"} describes the number (this associates distinct numbers to "all" finite sets of natural numbers); then comparison of "k"-combinations can be done by comparing the associated binary numbers. In the example "C" and "C"<nowiki>'</nowiki> correspond to numbers 1001011001 =