Lattice theory

Pseudocomplement

In mathematics, particularly in order theory, a pseudocomplement is one generalization of the notion of complement. In a lattice L with bottom element 0, an element x ∈ L is said to have a pseudocomplement if there exists a greatest element x* ∈ L with the property that x ∧ x* = 0. More formally, x* = max{ y ∈ L | x ∧ y = 0 }. The lattice L itself is called a pseudocomplemented lattice if every element of L is pseudocomplemented. Every pseudocomplemented lattice is necessarily bounded, i.e. it has a 1 as well. Since the pseudocomplement is unique by definition (if it exists), a pseudocomplemented lattice can be endowed with a unary operation * mapping every element to its pseudocomplement; this structure is sometimes called a p-algebra. However this latter term may have other meanings in other areas of mathematics. (Wikipedia).

Video thumbnail

Teach Astronomy - Pseudoscience

http://www.teachastronomy.com/ A pseudoscience is something that pretends to be scientific but is not. Science follows a rigorous method which relies on the sharing of data, the basis in observations, and the fact that any scientist can assert something, but it has to be supported by evid

From playlist 01. Fundamentals of Science and Astronomy

Video thumbnail

What is an Injective Function? Definition and Explanation

An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez

From playlist Functions

Video thumbnail

Definition of an Injective Function and Sample Proof

We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil

From playlist Injective, Surjective, and Bijective Functions

Video thumbnail

Why You Should Never Say "It's Just A Theory"

A portion of our culture distrusts the scientific method, assuming that there are transcendent truths unknowable by science. But nothing is truly out of bounds for science. If it's real, it can be studied, and tested. Perhaps the greatest misunderstanding our culture has about the scientif

From playlist Science for Common Folk

Video thumbnail

Underactive thyroid.mov

An general explanation of the underactive thyroid.

From playlist For Patients

Video thumbnail

Determining the negation of a hypothesis and conclusion from a statement

👉 Learn how to find the negation of a statement. The negation of a statement is the opposite of the statement. It is the 'not' of a statement. If a statement is represented by p, then the negation is represented by ~p. For example, The statement "It is raining" has a negation of "It is not

From playlist Negation of a Statement

Video thumbnail

How I learned to love pseudoscience

Check out Brian Keating's channel: https://www.youtube.com/channel/UCmXH_moPhfkqCk6S3b9RWuw and have a look at his new book, Think Like a Nobel Prize Winner: https://urlgeni.us/amzn/TLANPW As a scientist, I spend a lot of time fighting pseudoscience. But I have come to think that pseudosc

From playlist Philosophy of Science

Video thumbnail

Definition of a Surjective Function and a Function that is NOT Surjective

We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht

From playlist Injective, Surjective, and Bijective Functions

Video thumbnail

What is the negation of a statement and examples

👉 Learn how to find the negation of a statement. The negation of a statement is the opposite of the statement. It is the 'not' of a statement. If a statement is represented by p, then the negation is represented by ~p. For example, The statement "It is raining" has a negation of "It is not

From playlist Negation of a Statement

Video thumbnail

Find and classify the discontinuity of the rational function

👉 Learn how to classify the discontinuity of a function. A function is said to be discontinuos if there is a gap in the graph of the function. Some discontinuities are removable while others are non-removable. There is also jump discontinuity. A discontinuity is removable when the denomin

From playlist Holes and Asymptotes of Rational Functions

Related pages

Order theory | Interior (topology) | Filter (mathematics) | Topological space | Dense set | Variety (universal algebra) | Bounded set | Mathematics | Complemented lattice | Stone algebra | Topology | Binary operation | Heyting algebra | Distributive lattice | Closure operator | Lattice (order) | Boolean algebra (structure)