Sentence examples for ordinary algebra from inspiring English sources

The foregoing definitions and the well-known properties of scalar numbers (represented by s and t) show that Inasmuch as the laws (1), (2), and (3) are identical with those encountered in ordinary algebra, it is quite proper to use familiar algebraic rules to solve systems of linear equations containing vectors.

Up to this point his sole focus was to show that Aristotelian logic could be handled by simple algebraic methods, mainly through the use of an elimination theorem borrowed from ordinary algebra.

But this week, ordinary algebra reasserted itself.

In ordinary algebra, it was the use of negative numbers and imaginary numbers that caused concern.

The answer is simple: the law x + x = x would have destroyed his ability to use ordinary algebra: from x + x = x one has, by ordinary algebra, x = 0.

He said this was the way ordinary algebra worked with the uninterpretable $\sqrt{-1}$\sqrt{-1}$rootoft of −1.

It is important to observe that [ ϕ 1 ] induces an algebra homomorphism H ∗ (A ) to H ∗ (B ) so that cohomology is a functor from A ∞ -algebras to ordinary algebras.

Insights from category theory, in particular the expression of a variety as a monad, defined as a monoid object in the category CC of endofunctors of a category C (Set in the case of ordinary universal algebra) indicate that a cleaner and more general notion of variety is obtained when the operations can form a proper class.

A glossary of the commonly used mathematical notation would eliminate the need to search for the initial description and be an additional tool for those of us still learning to master linear algebra, ordinary calculus, and calculus of variations.

These geometries are classified by three kinds of the Kac Moody algebras: ordinary, i.e. finite dimensional, affine and indefinite.

Let be considered as a real unital abelian Banach algebra under ordinary complex multiplication and whose norm is the absolute value.