Dialetheism (from Greek δι- di- 'twice' and ἀλήθεια alḗtheia 'truth') is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called "true contradictions", dialetheia, or nondualisms. Dialetheism is not a system of formal logic; instead, it is a thesis about truth that influences the construction of a formal logic, often based on pre-existing systems. Introducing dialetheism has various consequences, depending on the theory into which it is introduced. A common mistake resulting from this is to reject dialetheism on the basis that, in traditional systems of logic (e.g., classical logic and intuitionistic logic), every statement becomes a theorem if a contradiction is true, trivialising such systems when dialetheism is included as an axiom. Other logical systems, however, do not explode in this manner when contradictions are introduced; such contradiction-tolerant systems are known as paraconsistent logics. Dialetheists who do not want to allow that every statement is true are free to favour these over traditional, explosive logics. Graham Priest defines dialetheism as the view that there are true contradictions. Jc Beall is another advocate; his position differs from Priest's in advocating constructive (methodological) deflationism regarding the truth predicate. (Wikipedia).
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Number theory Full Course [A to Z]
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio
From playlist Number Theory
(New Version Available) Inverse Functions
New Version: https://youtu.be/q6y0ToEhT1E Define an inverse function. Determine if a function as an inverse function. Determine inverse functions. http://mathispower4u.wordpress.com/
From playlist Exponential and Logarithmic Expressions and Equations
How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y
From playlist Introducing linear algebra
Trigonometric Functions: Angles of Any Magnitude (1 of 2: The unit circle)
More resources available at www.misterwootube.com
From playlist Trigonometry and Measure of Angles
Visualizing decimal numbers and their arithmetic 67 | Arithmetic and Geometry Math Foundations
This video gives a precise definition of a decimal number as a special kind of rational number; one for which there is an expression a/b where a and b are integers, with b a power of ten. For such a number we can extend the Hindu-Arabic notation for integers by introducing the decimal form
From playlist Math Foundations
How to Solve Trigonometric Equations (Precalculus - Trigonometry 22)
A very In-Depth look into solving equations that involve trig functions. We will focus on solving equations without having to use inverse trigonometric functions and relating solutions to the unit circle. Support: https://www.patreon.com/ProfessorLeonard
From playlist Precalculus - College Algebra/Trigonometry
Trigonometry 6 The Sine of the Sum and the Difference of Two Angles
A description of the sine function of the sum and difference of two angles.
From playlist Trigonometry
Solving Trigonometric Equations
We solved so many equations when studying algebra. Now that we understand trig functions, as well as inverse trig functions, we are ready to solve trigonometric equations. This will combine an understanding of trigonometry with some of the techniques we learned in algebra, and in the end,
From playlist Trigonometry