Definition of Invariant

An invariant is a property, condition, or a constraint that remains consistent, static, or unchanging throughout a specific context, situation, or process.

Key attributes of an invariant:

• Consistency: Invariants do not change over time or in different circumstances.
• Stability: Invariants remain fixed and do not fluctuate within a given system or scenario.
• Unchanging: Invariants are not affected by any transformations, operations, or alterations applied to the related objects or variables.
• Preservation: Invariants are maintained and enforced throughout the execution of a process, algorithm, or program.

Examples of invariants:

1. In a conservation law, such as the law of energy conservation, the total energy in a closed system remains constant over time.

2. In a bank account, the total balance should remain unchanged after performing a series of deposits and withdrawals.

3. In a sorting algorithm, a sorted array will always maintain the property of having every element in a higher position than the element before it.

Importance of invariants:

By identifying and utilizing invariants, we can ensure the integrity, reliability, and correctness of systems, processes, or algorithms. Invariants act as valuable guidelines for designing, implementing, and verifying various aspects of software, hardware, scientific principles, and mathematical models.