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The way that a regular expression describes a regular language The concatenation of ab a b and ba b a is, then, just abba a b b a - a word of length 4 Monoids This endows X∗ X ∗ with the structure of an algebra that has a product operation (concatenation) and an identity (the empty word) that satisfy the equations:
Simplification of the sum of all 4-digit palindromic numbers 1 I apologize for the simplicity of this question, if necessary I understand that the sum of all 4-digit palindromes is as follows: $$\sum_ {a=1}^ {9} (\sum_ {b=0}^ {9}abba),$$ which can be further expanded upon such that:
Uncountable vs Countable Infinity - Mathematics Stack Exchange My friend and I were discussing infinity and stuff about it and ran into some disagreements regarding countable and uncountable infinity As far as I understand, the list of all natural numbers is
Commutator Subgroup of $D_8$ - Mathematics Stack Exchange For instance, we have $$aba^ {-1}b^ {-1} = aba^3b = abba = a^2$$ You can calculate the commutator of any other two elements as well, but they will all give you either $a^2$ or $e$
Probability of tie - Mathematics Stack Exchange But how I see it, with 4 persons there are 13 ways of leading the votation to a Tie AABB ABBA ABAB BBAA BABA ABCC BACC CCBA CCAB ACBC BCAC ACCB BCCA so there are 13 over $3^4$ so $\frac {13} {3^4}$
elementary number theory - Divisibility Tests for Palindromes . . . I've found and proven the following extensions to palindromes of the usual divisibility rules for 3 and 9: A palindrome is divisible by 27 if and only if its digit sum is A palindrome is divisible by 81 if and only if its digit sum is This doesn't straightforwardly extend to 243 As an example, using this you can immediately see the smallest palindromic multiple of 81 is 999999999, and the