**Example 1:**
Consider the numbers (4^n), where (n) is a natural number. Define a function
[
f(n) = 4^n
]
Analyze (+) the behavior of this function and investigate (*) the pattern of its last digit.
Is there any value of (n \in \mathbb{N}) such that (4^n) ends with the digit zero (0)?
Use logical steps enclosed in brackets ( ), square brackets [ ], and curly braces { } to organize your reasoning. Clearly show division /, multiplication *, addition +, and subtraction - where needed.
You may use the following symbols as part of structured explanation:
* Caret ( ^ ) for powers
* Backslash ( \ ) or forward slash ( / ) for steps or division
* Pipe ( | ) to separate ideas
* Colon ( : ) and semicolon ( ; ) to explain steps
* Question mark ( ? ) to state the problem
* Exclamation mark ( ! ) for conclusions
* At sign ( @ ), hash ( # ), dollar ( $ ), percent ( % ), ampersand ( & ), and underscore ( _ ) as labels or markers
Avoid incorrect assumptions and present your reasoning clearly using proper mathematical structure.
"The value of the function applied **twice** at 0 is greater than the value of the function applied **once** at 0."
### Step-by-step breakdown:
- : apply the function to 0
- : take the result and plug it **again** into the function
So it's like:
1. First compute
2. Then compute
3. Compare: is f(a) > a?
### Simple example
Let's say:
Then:
-
-
So:
2 > 1 \quad \checkmark \text{true}