rfvilla.blogg.se - Approximately equal symbol in mathematica

For exact numeric quantities, Equal uses numerical approximations to establish inequality, which can be affected by the value of the global variable $Ma圎xtraPrecision. For example, 1.01`2=1 returns True, while 1.01`3=1 returns False.

Equality for numbers below machine precision is established based on agreement to within the precision of the lowest precision number. Numbers with machine precision ( MachinePrecision) or greater are considered equal if they differ in at most their last seven binary digits.The single-argument form Equal returns True (as, slightly paradoxically, does the single-argument form Unequal ). The multiple-argument form Equal, which may also be input as expr 1= expr 2  …, returns True if all expressions expr i are numerically equal, False if at least two are not equal and unevaluated otherwise. Equal may be input using double equal signs as expr 1= expr 2 or using the \ character as expr 1 expr 2. For example, Equal )/2, GoldenRatio ] returns True, Equal returns False and Equal returns unevaluated. Equal returns True if expr 1 and expr 2 are numerically equal, False if they are unequal and unevaluated if equality cannot be established.In TraditionalForm, lhs= rhs is output as lhs  rhs.

It can also be input as \ or lhs  rhs.

In StandardForm and InputForm, lhs= rhs can be input as lhs \ rhs or lhs  rhs.

Equal remains unevaluated when lhs or rhs contains objects such as Indeterminate and Overflow.

This process can be affected by the setting of the global variable $Ma圎xtraPrecision.

For exact numeric quantities, Equal internally uses numerical approximations to establish inequality.

e 1= e 2= e 3 gives True if all the e i are equal.

For numbers below machine precision, the required tolerance is reduced in proportion to the precision of the numbers.

Approximate numbers with machine precision or higher are considered equal if they differ in at most their last seven binary digits (roughly their last two decimal digits).

lhs= rhs returns False if lhs and rhs are determined to be unequal by comparisons between numbers or other raw data, such as strings.

lhs= rhs returns True if lhs and rhs are ordinary identical expressions.

lhs= rhs is used to represent a symbolic equation, to be manipulated using functions like Solve.