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There is not "the" conjecture: there are several.
The oldest and probably best known unsolved conjecture in number theory is the Goldbach conjecture. According to it every even integer greater than two can be expressed as the sum of two prime numbers.
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Why do you need conjectures in math?
Because mathematics is a axiomatic system so that every new statement remains a conjecture until it is proved.
Are conjectures allowed in proofs?
Usually not. If you do use conjectures, you should make it quite clear that the proof stands and falls with the truth of the conjecture. That is, if the conjecture happens to be false, then the proof of your statement turns out to be invalid.
How do you use the ideas of logic with conditional if-then statements to verify valid conjectures and refute invalid conjectures?
By creating a strong inference, you can then put your ideas to the test. After close observation, you can then rule-out any incorrect guesses.
What is a reasoning process that involves looking for patterns and making conjectures?
Inductive Reasoning
What kind of statement is a conjecture?
A conjecture is a statement that is believed to be true, but has yet to be proven. Conjectures can often be disproven by a counter example and are then referred to as false conjectures.
What is the hardiest math problem of all?
That would most likely be one of the many as yet unproven conjectures that are believed to have proofs.
Do conjectures explain a proof?
No. Conjectures are "good" guesses.
Why do you need conjectures in math?
Because mathematics is a axiomatic system so that every new statement remains a conjecture until it is proved.
In geometry you can use deductive rules to?
In geometry, deductive rules can be used to prove conjectures.
Fill in the blank In geometry youll often be able to use deductive rules to conjectures?
prove conjectures
How do you use the ideas of direct and indirect proof along with algebraic properties to verify valid conjectures and refute invalid conjectures?
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What rhymes with lectures?
Some words that rhyme with "lectures" are textures, conjectures, and ruptures.
What is the complete definition of math?
Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.
What word is closely related to conjectures?
surmises
What type of thinking do you use to make conjectures?
inductive
What must be testable and capable of being proven false?
hypotheses or more generally conjectures should be capable of being refuted see: Karl Popper - Conjectures and Refutations
What is the definition geometry conjecture?
Twenty Conjectures in Geometry:Vertical Angle Conjecture: Non-adjacent angles formed by two intersecting lines.Linear Pair Conjecture: Adjacent angles formed by two intersecting lines.Triangle Sum Conjecture: Sum of the measures of the three angles in a triangle.Quadrilateral Sum Conjecture: Sum of the four angles in a convex four-sided figure.Polygon Sum Conjecture: Sum of the angles for any convex polygon.Exterior Angles Conjecture: Sum of exterior angles for any convex polygon.Isosceles Triangle Conjectures: Isosceles triangles have equal base angles.Isosceles Trapezoid Conjecture: Isosceles trapezoids have equal base angles.Midsegment Conjectures: Lengths of midsegments for triangles and trapezoids.Parallel Lines Conjectures: Corresponding, alternate interior, and alternate exterior angles.Parallelogram Conjectures: Side, angle, and diagonal relationships.Rhombus Conjectures: Side, angle, and diagonal relationships.Rectangle Conjectures: Side, angle, and diagonal relationships.Congruent Chord Conjectures: Congruent chords intercept congruent arcs.Chord Bisector Conjecture: The bisector of a chord passes through the center of the circle.Tangents to Circles Conjectures: A tangent to a circle is perpendicular to the radius.Inscribed Angle Conjectures: An inscribed angles has half the measure of intercepted arc.Inscribed Quadrilateral Conjecture: Opposite angles are supplements.The Number "Pi" Conjectures: Circumference and diameter relationship for a circle.Arc Length Conjecture: Formula to calculate the length of an arc on a circle.
