- published: 02 Oct 2015
- views: 3920613
In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements ), and the number of ordered element (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. A sequence is a discrete function.
For example, (C, R, Y) is a sequence of letters that differs from (Y, C, R), as the ordering matters. Sequences can be finite, as in this example, or infinite, such as the sequence of all even positive integers (2, 4, 6,...). Finite sequences are sometimes known as strings or words and infinite sequences as streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.
There are various and quite different notions of sequences in mathematics, some of which (e.g., exact sequence) are not covered by the notations introduced below.
In addition to identifying the elements of a sequence by their position, such as "the 3rd element", elements may be given names for convenient referencing. For example a sequence might be written as (a1, a2, a3, … ), or (b0, b1, b2, … ), or (c0, c2, c4, … ), depending on what is useful in the application.
i've been waiting all night
watching as this moonlight shines through your hair
and tell me this will never last
just tell me this is in the past
cause i'm all yours my dear
and you say, say that you were ready
but we know, you were never ready for whats to come
and watching from your window
thats all i can do
till hes done
till hes done with you
and i'm so impressed
by the way that she moves her hands down my chest
is this love again?
so go on
describing how i make you feel
cause its all i wanna hear
well maybe you're right
maybe now is not the time
for just a whisper of the things
that we hold dear
and maybe stars will grace your sky
like open arms and wonder why
she cries inside
bring these walls down again
cause i don't know where she goes