A sequence can be start by the a2term?

[erogol]

Can i define a sequence which starts with a2. term or i must define the first term a1 as well

 

[mathman]

You can call the first term anything you want. It is merely a label.

 

[poutsos.A]

Can i define a sequence which starts with a2. term or i must define the first term a1 as well

A sequence of real Nos is a function ,from the natural Nos N to the real Nos R.

But a function from N TO R IS according to the definition of a function a subset of NxR ,such that for all nεN ,there exists a unique xεR ,SUCH that (n,x) BELONGS to the function.

So if you ignore the 1st member ,strictly speaking you go against the definition of the sequence

 

[Focus]

A sequence of real Nos is a function ,from the natural Nos N to the real Nos R.

But a function from N TO R IS according to the definition of a function a subset of NxR ,such that for all nεN ,there exists a unique xεR ,SUCH that (n,x) BELONGS to the function.

So if you ignore the 1st member ,strictly speaking you go against the definition of the sequence

Not really, \{a_n\}_{n=1}^\infty \backslash \{a_1\} is still a sequence, just take the map n \mapsto a_{n+1}. It is perfectly well defined.

 

[poutsos.A]

Not really, \{a_n\}_{n=1}^\infty \backslash \{a_1\} is still a sequence, just take the map n \mapsto a_{n+1}. It is perfectly well defined.

What you have written is a subsequence of the sequence {a_{n}}.So if you start the sequence { a_{n}} from the No 2 ,lets say , the subsequence will start from ,2 as well ,hence violating the definition of the sequence

 

[Focus]

What you have written is a subsequence of the sequence {a_{n}}.So if you start the sequence { a_{n}} from the No 2 ,lets say , the subsequence will start from ,2 as well ,hence violating the definition of the sequence

Did you even read my post? It fits your definition perfectly.

 

[poutsos.A]

Use the definition of the subsequence correctly