Less-than sign been repurposed for a range of uses and operations. The less-than sign (<) is an original ASCII character (hex 3C, decimal 60). The less-than sign is used for an approximation of the opening angle bracket (⟨). ASCII does not have angle brackets. In BASIC, Lisp-family languages, and C-family languages (including Java and C++), operator < means "less than". In Coldfusion, operator .lt. means "less than". In Fortran, operator .LT. means "less than"; later versions allow <. In Bourne shell, operator -lt means "less than". The double less-than sign («) is used for an approximation of the much-less-than sign (≪) or
Degrees of freedom (statistics) the vectors of residuals are constrained to lie in a space of smaller dimension than the number of components in the vector. That smaller dimension is the number of degrees of freedom for error, also called residual degrees of freedom. Perhaps the simplest example is this. Suppose are random variables each with expected value μ, and let be the "sample mean." Then the quantities are residuals that may be considered estimates of the errors "X" − μ. The sum of the residuals (unlike the sum of the errors) is necessarily 0. If one knows the values of any "n" −