Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Exponentiation
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
===Combinatorial interpretation=== {{See also|#Exponentiation over sets|l1=Exponentiation over sets}} For nonnegative integers {{mvar|n}} and {{mvar|m}}, the value of {{math|''n''<sup>''m''</sup>}} is the number of [[function (mathematics)|functions]] from a [[set (mathematics)|set]] of {{mvar|m}} elements to a set of {{mvar|n}} elements (see [[cardinal exponentiation]]). Such functions can be represented as {{mvar|m}}-[[tuple]]s from an {{mvar|n}}-element set (or as {{mvar|m}}-letter words from an {{mvar|n}}-letter alphabet). Some examples for particular values of {{mvar|m}} and {{mvar|n}} are given in the following table: {| class="wikitable" !{{math|''n''<sup>''m''</sup>}} !The {{math|''n''<sup>''m''</sup>}} possible {{mvar|m}}-tuples of elements from the set {{math|{{mset|1, ..., ''n''}}}} |- |0{{sup|5}} = 0 |{{CNone|none}} |- |1{{sup|4}} = 1 |(1, 1, 1, 1) |- |2{{sup|3}} = 8 |(1, 1, 1), (1, 1, 2), (1, 2, 1), (1, 2, 2), (2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2) |- |3{{sup|2}} = 9 |(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3) |- |4{{sup|1}} = 4 |(1), (2), (3), (4) |- |5{{sup|0}} = 1 |() |}
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)