Predicate logic | Propositions
In mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values: As the free variables of a (general) formula can range over several values, the truth value of such a formula may vary. Sentences without any logical connectives or quantifiers in them are known as atomic sentences; by analogy to atomic formula. Sentences are then built up out of atomic formulas by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory. For first-order theories, interpretations are commonly called structures. Given a structure or interpretation, a sentence will have a fixed truth value. A theory is satisfiable when it is possible to present an interpretation in which all of its sentences are true. The study of algorithms to automatically discover interpretations of theories that render all sentences as being true is known as the satisfiability modulo theories problem. (Wikipedia).
Evaluate an equation by substitution
👉 Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)
From playlist Simplify Expressions Using Order of Operations
Evaluate an expression with one variable ex2, 2x + 3 - 2; x=5
👉 Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)
From playlist Simplify Expressions Using Order of Operations
How to evaluate an expression three terms
👉 Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)
From playlist Simplify Expressions Using Order of Operations
Evaluating an expression with one variable ex 7, w^2 - 3w + 10; w = 4
👉 Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)
From playlist Simplify Expressions Using Order of Operations
Evaluating an expression with one variable ex 3, (2x - 4)/4x; x = -3
👉 Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)
From playlist Simplify Expressions Using Order of Operations
Evaluate an expression with one variable ex 5, 2(x - 3) - 5; x=-1
👉 Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)
From playlist Simplify Expressions Using Order of Operations
I still don't get it evaluating expressions
👉 Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)
From playlist Simplify Expressions Using Order of Operations
Evaluating an expression with one variable ex 8, (-x^2 +1)/3; x = 3
👉 Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)
From playlist Simplify Expressions Using Order of Operations
Evaluating an expression with two variables ex 5, (bc)^2; b = 4; c = 8
👉 Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)
From playlist Simplify Expressions Using Order of Operations
Gödel's Incompleteness Theorems: An Informal Introduction to Formal Logic #SoME2
My entry into SoME2. Also, my first ever video. I hope you enjoy. The Book List: Logic by Paul Tomassi A very good first textbook. Quite slow at first and its treatment of first-order logic leaves a little to be desired in my opinion, but very good on context, i.e. why formal logic is im
From playlist Summer of Math Exposition 2 videos
Logic: The Structure of Reason
As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be
From playlist Logic & Philosophy of Mathematics
IMS Public Lecture: Logic and Computation
Ted Slaman, University of California, Berkeley, USA
From playlist Public Lectures
Inference: A Logical-Philosophical Perspective with Alexander Paseau
In this talk, Professor Alexander Paseau, Faculty of Philosophy, University of Oxford, will describe some of his work on inference within mathematics and more generally. Inferences can be usefully divided into deductive or non-deductive. Formal logic studies deductive inference, the obviou
From playlist Franke Program in Science and the Humanities
Mathematik für alle - in Zeiten von Corona, Folge 1: Was ist Mathematik?
Was Sie schon immer über Mathematik wissen wollten, aber nie zu fragen wagten Nicht nur die Virologie, auch die Mathematik ist derzeit in aller Munde. Es wird von linearem und exponentiellem Wachstum gesprochen, von dynamischen Systemen, von Statistiken und Korrelationen, validen Testverf
From playlist Mathematik für alle - in Zeiten von Corona
Start Learning Logic - Part 1 - Logical Statements, Negation and Conjunction [dark version]
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Or support me via PayPal: https://paypal.me/brightmaths Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics Or via Patreon: https://www.patreon.com/bsom Or via other methods: https://thebrightsideofmathematics.
From playlist Start Learning Mathematics [dark version]
Intro to the Philosophy of Mathematics (Ray Monk)
A good introduction to the philosophy of mathematics by Ray Monk. He considers the issue of the nature of mathematical truth - what mathematics is actually about - and discusses the views of Plato, Aristotle, Kant, Frege and Russell. What is mathematics about? Is mathematics something disc
From playlist Logic & Philosophy of Mathematics
We present the three main logical operations: and, or, not. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.e
From playlist Proof Writing
Jason Rosenhouse - Raymond Smullyan's Mathematics - G4G13 Apr 2018
I give an overview of Smullyan's mathematical research
From playlist G4G13 Videos
Evaluating an expression with one variable ex 6, (3p - 5)^2; p = 3
👉 Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)
From playlist Simplify Expressions Using Order of Operations