# Times

x*y*z, x×y×z, or x y z

represents a product of terms.

# Details

• The character × is entered as * or \[Times]. It is not the same as \[Cross].
• Times has attributes Flat, Orderless, and OneIdentity.
• The default value for arguments of Times, as used in x_. patterns, is 1.
• Times[] is taken to be 1.
• Times[x] is x.
• 0x evaluates to 0, and 0.0x evaluates to 0.0.
• Unlike other functions, Times applies builtin rules before userdefined ones. As a result, it is not possible to make definitions such as 2*2=5.

# Background & Context

• Times is a function that does multiplication (takes the product) of expressions. The expression Times[a,b,c,] is commonly represented using the shorthand syntax a*b*c*, a×b×c×, or simply a b c . Special cases include Times[], which is taken to be 1, and Times[x], which is taken to be x.
• Times sorts its arguments and collapses any terms of the same type. Times also threads element-wise over lists. Expand can be used to expand out products of expressions not automatically multiplied out by Times.
• TimesBy can be used to multiply the value of a given variable. Divide gives the division of two expressions.
• Multiplication of a function over a range or list of arguments is done using the function Product. Other types of multiplication include Dot (for matrix or vector multiplication) and NonCommutativeMultiply (for non-commuting products).

# Examples

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## Basic Examples(3)

Enter Times with spaces; × is added automatically between numbers:

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Alternative form:

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Times threads element-wise over lists:

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Explicit FullForm:

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