Subsequently vs. Consequently

Subsequently

In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. For example, the sequence

⟨

A

,

B

,

D

⟩

{displaystyle langle A,B,Drangle }

is a subsequence of

⟨

A

,

B

,

C

,

D

,

E

,

F

⟩

{displaystyle langle A,B,C,D,E,Frangle }

obtained after removal of elements

C

{displaystyle C}

,

E

{displaystyle E}

, and

F

{displaystyle F}

. The relation of one sequence being the subsequence of another is a preorder.

The subsequence should not be confused with substring

⟨

A

,

B

,

C

,

D

⟩

{displaystyle langle A,B,C,Drangle }

which can be derived from the above string

⟨

A

,

B

,

C

,

D

,

E

,

F

⟩

{displaystyle langle A,B,C,D,E,Frangle }

by deleting substring

⟨

E

,

F

⟩

{displaystyle langle E,Frangle }

. The substring is a refinement of the subsequence.

The list of all subsequences for the word “apple” would be “e, l, le, p, pe, pl, ple, p, pe, pl, ple, pp, ppe, ppl, pple, a, ae, al, ale, ap, ape, apl, aple, ap, ape, apl, aple, app, appe, appl, apple”.