A Theorem is a major result; A Corollary is a theorem that follows on from another theorem; A Lemma is a small result (less important than a theorem) Examples. Here is an example from Geometry:

This is a list of notable theorems. Lists of theorems and similar statements include: Most of the results below come from pure mathematics, but some are from theoretical physics, economics, and other applied fields.

Theorem 1: If two lines intersect, then they intersect in exactly one point. Theorem 2: If a point lies outside a line, then exactly one plane contains both the line and the point. Theorem 3: If two lines intersect, then exactly one plane contains both lines.

Study with Quizlet and memorize flashcards containing terms like Vertical Angles Theorem, Congruent Supplements Theorem, Congruent Complements Theorem and more.

Theorem 1.7.5: If the exterior sides of two adjacent angles form perpendicular rays, then theses angles are complementary. Theorem 2.1.1 : From a point not on a given line, there is exactly one line

Theorem 5: The opposite angles in a cyclic quadrilateral are supplementary. All congruent figures are similar, but it doesn’t mean that all similar figures are congruent. Two polygons with the same number of sides are similar if their corresponding angles are equal, and their corresponding sides are in the same ratio.

The angle subtended by an arc at the centre of a circle is double the size of the angle subtended by the same arc at the circle (on the same side of the chord as the centre). Z at centre = 2 at circumference wth O AB at BOC-2BAC AO Proof: In A B C: OA = oe L of A] . In A C: …

To the first point: you have $k$-linear maps $\theta\colon A \to k^n$ and $\theta'\colon {\frak a}/{\frak a^2} \to k^n$ and the second an isomorphism, so to compute the dimension of $\theta(\mathfrak{b})$ you could instead compute the dimension of $\theta'^{-1}(\theta(\mathfrak{b}))$.

I was reading Friedberg Linear Algebra after Axler and I noticed that Friedberg says the span of any subset S but Axler says the span of a LIST of vectors $v_1,..,v_n$. The question is: Is Friedberg making an implicit assumption in the proof that …

Given two integers a and b we say a divides b if there is an integer c such that b = ac. If a divides b, we write ajb. If a does not divide b, we write a6 jb. Example 1.1.1. The number 6 is divisible by 3, 3j6, since 6 = 3 2. Exercise 1.1.1. Let a, b, and c be …