What does trivial mean in math?

In mathematics, the adjective trivial is often used to refer to a claim or a case which can be readily obtained from context, or an object which possesses a simple structure (e.g., groups, topological spaces).

What is considered pure math?

Pure mathematics is the study of the basic concepts and structures that underlie mathematics. Traditionally, pure mathematics has been classified into three general fields: analysis, which deals with continuous aspects of mathematics; algebra, which deals with discrete aspects; and geometry.

What is a non trivial number?

A solution or example that is not trivial. Often, solutions or examples involving the number zero are considered trivial. Nonzero solutions or examples are considered nontrivial. For example, the equation x + 5y = 0 has the trivial solution (0, 0).

What is non-trivial in mathematics?

2 mathematics : having the value of at least one variable or term not equal to zero a nontrivial solution.

What is pure mathematics?

Pure mathematics is the study of the basic concepts and structures that underlie mathematics. Its purpose is to search for a deeper understanding and an expanded knowledge of mathematics itself.

Is pure mathematics useful in engineering education?

The case was made that pure mathematics is useful in engineering education: There is a training in habits of thought, points of view, and intellectual comprehension of ordinary engineering problems, which only the study of higher mathematics can give. An illustration of the Banach–Tarski paradox, a famous result in pure mathematics.

What are the uses of generality in pure mathematics?

One central concept in pure mathematics is the idea of generality; pure mathematics often exhibits a trend towards increased generality. Uses and advantages of generality include the following: Generalizing theorems or mathematical structures can lead to deeper understanding of the original theorems or structures

What kind of problems do pure mathematicians study?

There are many problems pursued by pure mathematicians that have their roots in concrete physical problems – particularly those that arise from relativity or quantum mechanics. Typically, in a deeper understanding of such phenomena, various “technicalities” arise (believe me when I tell you these technicalities are very difficult to explain).