**points**of

**continuity**are

**points**where a function exists, that it has some real value at that

**point**. Since the question emanates from the topic of ‘Limits’ it can be further added that a function exist at a

**point**‘a’ if limx→af(x) exists (means it has some real value.)

Just so, what is the definition of continuity at a point?

We can **define continuity at a point** on a **function** as follows: The **function** f is continuous at x = c if f (c) is **defined** and if. . In other words, a **function** is continuous at a **point** if the **function’s** value at that **point** is the same as the limit at that **point**.

what is continuity of a function? Definition of **Continuity** A **function** f(x) is said to be continuous at a point x = a, in its domain if the following three conditions are satisfied: f(a) exists (i.e. the value of f(a) is finite) Lim_{x}_{→}_{a} f(x) exists (i.e. the right-hand limit = left-hand limit, and both are finite)

One may also ask, what are the three conditions for continuity at a point?

**For a function to be continuous at a point from a given side, we need the following three conditions:**

- the function is defined at the point.
- the function has a limit from that side at that point.
- the one-sided limit equals the value of the function at the point.

What is the synonym of continuity?

**continuity**, persistence(noun) the property of a continuous and connected period of time. **Synonyms**: perseverance, tenacity, persistency, perseveration, persistence, doggedness, pertinacity, tenaciousness.