simplest calculations. The results of computer calculations are normally an approximation expressed in a limited number of significant digits, although they can be programmed to produce more precise results. Approximation can occur when a decimal number cannot be expressed in a finite number of binary digits. Related to approximation of functions is the asymptotic value of a function, i.e. the value as one or more of a function's parameters becomes arbitrarily large. For example, the sum (k/2)+(k/4)+(k/8)+...(k/2^n) is asymptotically equal to k. No consistent notation is used throughout mathematics and some texts use ≈ to mean approximately equal and ~ to mean asymptotically equal whereas other texts use the symbols the other way around. Typography The approximately equals sign, ≈, was introduced by British mathematician Alfred Greenhill. LaTeX symbols Symbols used in LaTeX markup. (\approx), usually to indicate approximation between numbers, like . (\not\approx), usually to indicate that numbers are not approximately equal (1 2). (\simeq), usually to indicate asymptotic equivalence between functions, like . So writing would be wrong under this definition, despite wide use. (\sim), usually to indicate proportionality between functions, the same of the line above will be . (\cong), usually to indicate congruence between figures, like . (\eqsim), usually to indicate that two quantities are equal up to constants. (\lessapprox) and (\gtrapprox), usually to indicate that either the inequality holds or the two values are approximately equal. Unicode Symbols used to denote items that are approximately equal are wavy or dotted equals signs. : which is also sometimes used to indicate proportionality : which is also sometimes used to indicate proportionality : another combination of "≈" and "=", which is used to indicate isomorphism or congruence : yet another combination of "≈" and "=", used to indicate equivalence or approximate equivalence : which can be used to represent the approach of a variable, , to a limit; like the common syntax, ≐ 0 : which is used like "≈" or "≃" in Japan, Taiwan, and Korea : a reversed variation of Science Approximation arises naturally in scientific experiments. The predictions of a scientific theory can differ from actual measurements. This can be because there are factors in the real situation that are not included in the theory. For example, simple calculations may not include the effect of air resistance. Under these circumstances, the theory is an approximation to reality. Differences may also arise because of limitations