# What's the specific difference between lemma and algorithms?

Lemma and theorem are formally the same. A lemma is an intermediate theorem in proof and an algorithm is a set of rules that are to be followed to reach a certain result.

## Answer: An algorithm is a list of well-defined steps for achieving a task and a lemma (or theorem) is a proven statement that can be used for solving larger problems.

Go through the steps to understand the key points of difference.

**Explanation:**

The basic difference between lemma and algorithms:

A proven statement that is used for proving other statements is called a lemma.

A series of well-defined steps that are used to prove or solve a problem is called an algorithm. Formally these two have the same set of patterns but exhibit in a different sense.

Let us consider Euclid's division lemma as an example.

For a pair of given positive integers ‘a’ and ‘b’, there exist unique integers ‘q’ and ‘r’ such that a = bq + r, where, 0 < r < b

### An algorithm is a list of well-defined steps for achieving a task and a lemma (or theorem) is a proven statement that can be used for solving larger problems.

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