```typescript
/** Safe division function that throws errors for invalid inputs. */
export function safeDivide(a: number, b: number): number {
  if (!Number.isFinite(a) || !Number.isFinite(b)) {
    throw new Error("Both arguments must be finite numbers.");
  }
  
  if (b === 0 || Number.isNaN(b)) {
    throw new Error("Division by zero or invalid number is not allowed.");
  }

  return a / b;
}
```