Carrier set

A carrier set \(X\) is a set of all possible elements of a sequence

Mathematical Definition

Let \(X\) be a (possibly infinite) set.

Examples

Binary Sequence

A binary sequence 0110100110

represented as

\(X = \{0,1\}\)

Musical Chorus Sequence

A musical chorus for Jingle bell rock

D                Dmaj7        D6
Jingle-bell, Jingle-bell, Jingle-bell Rock.
  D                D#dim
Jingle-bell swing and
 Em           A7     Em               A7            Em A7
Jingle-bell ring. Snowin' and blowin' up bushels of fun.
Em  A9                  A7
Now the jingle-hop has begun.

\(X = \{A7, A9, D, D6, Dmaj7, D\#dim, Em\}\)

DNA Sequence

A DNA sequence ATGCTAGCATGCTAGCATGCTAGC

\(X = \{A,C,G,T\}\)

English Text Sequence as char sequence

An English text sentence the quick brown fox jumps over the lazy dog

\(X = \{\ ,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z \}\)

English Text Sequence as word sequence

An English text sentence the quick brown fox jumps over the lazy dog

\(X = \{\ , brown, dog, quick, fox, lazy, over, the\}\)