math abc discrete functions 01

Math ABC - Discrete Functions 01

2021-06-06

What is Discrete Function?

A function whose domain is a discrete set is called a discrete function. The graph of a discrete function is a distinct set of points, not a smooth curve.

A sequence can be discrete function: A function whose domain is the set, or a subset, of the natural numbers and whose range is the terms of the sequence.

What is term of a sequence?

A single value or object in a sequence.

A sequence starts the term number 1, which means the 1st index number in a sequence is 1 but not 0.

Term Number, n	Term,tn
1	6
2	11
3	16
4	21

f(n) = 5n + 1 (n ∈ N)

What is explicit formula?

A formula that represents any term in a sequence relative to the term number n (n is a nature number N).

Discrete Function vs Continuous Function?

Disrete Function: Its graph is made up of separate points that are not connected.

Continuous Function: Its graph is a smooth curve with no holes or jumps. The function maps real numbers to real numbers.

A Bettery's charging level decreasing by day is a Continuous Function because the charging level decreases as time goes by.

Amount of a certain bacterial by hour (for exmaple: double every hour) is a Discrete Function because every 1 hour one bacterial can become two, but it can not be double at the middle time in a hour.