Smaller

Smaller

a < b represents the mathematical 'smaller than' relation. Use a << b to check it in a script.

Usages

a < b or Smaller[ a, b ]

a < b represents the inequality a < b, for example in a definition or an answer. In a script, it is not checked: 2 < 4 stays 2 < 4. It is checked when it is used as a condition in If or While, or inside Simplify.

Example in rendered
The inequality x < 4. x < 4 or Smaller[ x, 4 ] x<4x < 4
Example in out
Not checked in a script. 2 < 4 2 < 4
Checked inside Simplify. Simplify[ 2 < 4 ] True
Checked as a condition. a := 3
If[a < 4]
  r := 1
Else
  r := 0
End		 r = 1

a << b or SmallerEval[ a, b ]

a << b checks directly whether the value of a is smaller than the value of b, and returns True or False. If one of the values is not known, for example because it contains a variable, the comparison is left unevaluated.

Example in out
2 is smaller than 4. 2 << 4 True
2 is not smaller than 2. 2 << 2 False
Numerical values are compared. Pi << 3.15 True
A fraction and a decimal number. 1/3 << 0.3 False
Each element of a list is compared. {1, 5, 3} << 4 {True, False, True}
Quantities with the same unit. Quantity[2,'m'] << Quantity[3,'m'] True
Cannot be decided. x << 4 x << 4
Details
  • Different units: quantities with different units are not compared: Quantity[2,'m'] << Quantity[300,'cm'] is left unevaluated.
  • Undecided conditions: a condition in If that cannot be decided, such as y < 4 with y not defined, is treated as True.
  • Greater than: see Greater for a > b and a >> b.

See also: SmallerEqual, Greater, EqualsEval, UnequalsEval, If