A corollary is a statement that follows logically from a previously proven statement. It is a direct consequence of a previously proven theorem or lemma and can be seen as a simplified version of the original theorem.
For example, consider the statement "If a triangle has two sides of equal length, then it must be an isosceles triangle." This statement is a theorem that has been proven through logical reasoning.
Now consider the statement "If a triangle has two angles of equal measure, then it must be an isosceles triangle." This statement is a corollary of the original theorem, as it can be proven through logical reasoning based on the original theorem.
In other words, the second statement is a direct consequence of the first statement and can be seen as a simplified version of the original theorem.
Corollaries can be very useful in mathematics and other fields, as they allow us to derive new conclusions from previously proven statements without having to go through the entire proof process again. This can save a lot of time and effort, and helps to simplify complex ideas.
For example, consider the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem can be used to derive a number of corollaries, such as the fact that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse.
In conclusion, a corollary is a statement that follows logically from a previously proven statement and can be seen as a simplified version of the original theorem. Corollaries can be very useful in mathematics and other fields, as they allow us to derive new conclusions from previously proven statements without having to go through the entire proof process again.
Corollary in a Sentence
Since the item is moving, the brain recognizes that real motion has occurred. READ: What is the strongest concrete mix? Our concern lies with the first kind of Crusade, and with the other three only so far as they bear on the first, and as they illustrate the immense widening which the term "Crusade" now underwent - a widening accompanied by its inevitable corollary of shallowness of motive and degradation of impulse. The plot is only a corollary to the main thrust of the book, which is basically an extended development of Christopher's character. The use of the term corollary, rather than proposition or theorem, is intrinsically subjective. Just as we note similarities among people or events, we must also account for dissimilarities. When one object moves, it can result in the perception of another object moving.
Use corollary in a sentence
The Commonality Corollary Even though our individual constructs are unique to us, people do have experiences similar to others and in such cases have personal constructs similar to the constructs of other people. As a corollary to this decision it was determined that a large-scale monitoring program was required to detect possible changes in population trend. What is the plural of corollary? This objective, a corollary to the establishment of an integrated, frontier-free economic area, helps to give the idea of European citizenship its full meaning. A corollary of this is that the longer the distance from an urban center, the less efficient the municipal government. Belligerents, Brinkmanship, and the Big Stick: A Historical Encyclopedia of American Diplomatic Concepts, Santa Barbara: ABC Clio, 2009, p.
Kelly's personal construct theory and the 11 corollaries
What is the meaning of a corollary? This idea has as its corollary the possibility of ritually enacting the cosmic drama and, thus, of influencing those events in the cosmos that continuously affect human weal and woe. It sold fruit, such as bananas, from Latin America to Europe and the United States. The corollary being, if she slacks off, even a teensy bit, anything that goes wrong is her fault. They no not respond if the eyes of the money move. Sometimes American corporations practiced neo-colonialism. Clearly, the corollary must be true: if my life is in disorder, I will live forever.
Corollary
The Origin and Evolution of Corollary Corollary comes from the Late Latin noun corollarium, which can be translated as "a garland given as a reward. What is the difference between a theorem and a corollary? In addition, there are several more specific corollary conclusions to the main finding. What makes the eye think that something is moving when it really is not are the times when there is a 0% coherence in place. To create balance, the mind attempts to perceive motion in the opposite direction. A permeable construct allows new elements to penetrate or be admitted to the range of convenience. However, the corollary is not to do away with regulations, as implied by the conservatives.
