chore(docs): Supplement descriptions for defaulting loop indices to b…

…e `u64` (#3237)

Co-authored-by: José Pedro Sousa <[email protected]>
Co-authored-by: jfecher <[email protected]>

docs/docs/language_concepts/data_types/01_integers.md

@@ -15,9 +15,16 @@ keywords:
 An integer type is a range constrained field type. The Noir frontend currently supports unsigned,
 arbitrary-sized integer types.
 
+> **Note:** When an integer is defined in Noir without a specific type, it will default to `Field`. The one exception is for loop indices which default to `u64` since comparisons on `Field`s are not possible.
+
 An integer type is specified first with the letter `u`, indicating its unsigned nature, followed by
 its length in bits (e.g. `32`). For example, a `u32` variable can store a value in the range of
-$\\([0,2^{32}-1]\\)$:
+$\\([0,2^{32}-1]\\)$.
+
+> **Note:** The default proving backend supports both even (e.g. `u16`, `u48`) and odd (e.g. `u5`, `u3`)
+> sized integer types.
+
+Taking a look of how the type is used:
 
 ```rust
 fn main(x : Field, y : u32) {
@@ -28,6 +35,3 @@ fn main(x : Field, y : u32) {
 `x`, `y` and `z` are all private values in this example. However, `x` is a field while `y` and `z`
 are unsigned 32-bit integers. If `y` or `z` exceeds the range $\\([0,2^{32}-1]\\)$, proofs created
 will be rejected by the verifier.
-
-> **Note:** The default backend supports both even (e.g. `u16`, `u48`) and odd (e.g. `u5`, `u3`)
-> sized integer types.