What Defines the Nth Prime Number in Mathematics?

[grupah]

Dear Forum,

Does every sequence have a general term? What is the definition of the general term of a sequence?

Best wishes

 

[tiny-tim]

hi grupah!

a sequence is a function whose domain is the natural numbers (or a subset of them)

so we can write it as {a_n}_nεN,

and the general term of the sequence is a_n

(if you mean is there a straightforward formula for a_n, the answer is not necessarily, it depends how the sequence is defined)

 

[Millennial]

What is your definition of sequence, exactly?

 

[grupah]

Is it possible to represent all the terms of the sequence by the general term?

 

[tiny-tim]

i don't understand

can you give an example of what you're thinking of?​

 

[grupah]

Consider the sequence of prime numbers: {2,3,5,7,dots}
Does it have a general term?

 

[tiny-tim]

Consider the sequence of prime numbers: {2,3,5,7,dots}
Does it have a general term?

no, there's no formula (other than "a_n is the nth prime")

 

[grupah]

So, what is the mathematical definition of the general term, a kind of explanation?

 

[tiny-tim]

"the nth prime" is a mathematical definition!

it uniquely defines the number, and that's all maths requires