We give the definition of the kernel of a homomorphism, prove some of its properties, and give some examples. www.michael-penn.net www.randolphcollege.edu/mathem...
Injective is dual to surjective synthesizes bijective or isomorphism. Absolute truth is dual to relative truth -- Hume's fork. Absolute (isomorphism, same) is dual to relative (homomorphism, similarity). Same is dual to different.
Before (a priori, group) is dual to after (a posteriori, image) -- Immanuel Kant. Normal subgroups are dual to homomorphism (factor groups) synthesize the kernel. Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic. Being is dual to non-being creates becoming -- Plato. Domains (groups) are dual to codomains (image, range). Points are dual to lines -- the principle of duality in geometry. Null homotopic implies contraction to a point, non null homotopic requires at least two points (duality) -- topology. Polar opposites of the dyad unite into one or the monad - opposame. "Always two there are" -- Yoda.
@@emmpati There are patterns of duality hardwired into physics, mathematics & philosophy. Good news is dual to bad news. "Philosophy is dead" -- Stephen Hawking. Space is dual to time -- Einstein. Time dilation is dual to length contraction -- Einstein. Action is dual to reaction -- Sir Isaac Newton (the duality of forces). Attraction is dual to repulsion, push is dual to pull -- forces are dual in physics. There are 4 forces in physics, gravity, electromagnetism and the strong and weak forces -- interactions or forces are dual. If forces are dual then energy must be dual:- Energy = force * distance. Potential energy is dual to kinetic energy -- gravitational energy is dual. Energy is duality, duality is energy! Everything in physics is made from energy or duality! The council of Nicaea in 325 AD was set up to answer the question, is the Christ consciousness the same substance as God or a different substance? Same is dual to different, homo is dual to hetero. Thesis (God) is dual to anti-thesis (the Christ consciousness) creates the converging thesis or synthesis -- the time independent Hegelian dialectic. Questions are dual to answers. Christianity is based upon duality and not triality or trinity. If God & the Christ consciousness are made from energy then they are the same substance! Waves are dual to particles -- quantum duality. A dual process (syntropy) to that of increasing entropy constitutes a 4th law of thermodynamics! Making predictions to track targets, goals & objectives is a syntropic process -- teleological. Opposites, opposame (isomorphism) = duality (energy). The conservation of duality (energy) will be known as the 5th law of thermodynamics! "May the force (duality) be with you" -- Jedi teaching. "The force (duality) is strong in this one" -- Jedi teaching.
@@hyperduality2838 Einstein and Hawking are weak not only in terms of philosophy but also they are not important in physics. They are just famous. Hawking changed his 'thoughts' in every 3-5 years to sell his insignificant books. Continuity in physical tought along history of physics can be maintained without Einstein. He just combined little pieces of ideas circulating among his era's academia. It is very sad and scary, people are aware of nothing. Only being magazinal counts. When small people have long shadows, we approach to sun set
@@emmpati "Imagination is more important then knowledge" -- Einstein. "Through imagination and reason we turn experience into foresight (prediction)" -- Spinoza describing syntropy. The act of creating (emergence, synthesis, imagination) is a syntropic process. Creation is dual to destruction, annihilation. The one is defined in terms of the other. Antinomy (duality) is two truths that contradict each other -- Immanuel Kant. Increasing entropy causes you to update your predictions (syntropy) about the world around you and physicists make predictions all the time. Absolute truth is dual to relative truth -- Hume's fork. Thesis is dual to anti-thesis -- the Hegelian dialectic. Being is dual to non being creates becoming -- Plato. Duality leads to new laws of physics!
Thanks so much for your instruction! Your videos have been helping me a lot this term for my abstract algebra class
holy hell man! just what i was looking for great vid!
Injective is dual to surjective synthesizes bijective or isomorphism.
Absolute truth is dual to relative truth -- Hume's fork.
Absolute (isomorphism, same) is dual to relative (homomorphism, similarity).
Same is dual to different.
Thanks for the video.
reaaalllly helpfullll thanks
Great!
Before (a priori, group) is dual to after (a posteriori, image) -- Immanuel Kant.
Normal subgroups are dual to homomorphism (factor groups) synthesize the kernel.
Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic.
Being is dual to non-being creates becoming -- Plato.
Domains (groups) are dual to codomains (image, range).
Points are dual to lines -- the principle of duality in geometry.
Null homotopic implies contraction to a point, non null homotopic requires at least two points (duality) -- topology.
Polar opposites of the dyad unite into one or the monad - opposame.
"Always two there are" -- Yoda.
is philosophy dual to mathematics?
@@emmpati There are patterns of duality hardwired into physics, mathematics & philosophy.
Good news is dual to bad news.
"Philosophy is dead" -- Stephen Hawking.
Space is dual to time -- Einstein.
Time dilation is dual to length contraction -- Einstein.
Action is dual to reaction -- Sir Isaac Newton (the duality of forces).
Attraction is dual to repulsion, push is dual to pull -- forces are dual in physics.
There are 4 forces in physics, gravity, electromagnetism and the strong and weak forces -- interactions or forces are dual.
If forces are dual then energy must be dual:-
Energy = force * distance.
Potential energy is dual to kinetic energy -- gravitational energy is dual.
Energy is duality, duality is energy!
Everything in physics is made from energy or duality!
The council of Nicaea in 325 AD was set up to answer the question, is the Christ consciousness the same substance as God or a different substance?
Same is dual to different, homo is dual to hetero.
Thesis (God) is dual to anti-thesis (the Christ consciousness) creates the converging thesis or synthesis -- the time independent Hegelian dialectic.
Questions are dual to answers.
Christianity is based upon duality and not triality or trinity.
If God & the Christ consciousness are made from energy then they are the same substance!
Waves are dual to particles -- quantum duality.
A dual process (syntropy) to that of increasing entropy constitutes a 4th law of thermodynamics!
Making predictions to track targets, goals & objectives is a syntropic process -- teleological.
Opposites, opposame (isomorphism) = duality (energy).
The conservation of duality (energy) will be known as the 5th law of thermodynamics!
"May the force (duality) be with you" -- Jedi teaching.
"The force (duality) is strong in this one" -- Jedi teaching.
@@emmpati The word isomorphism actually means duality:- two differing descriptions of the same thing, "space" or state.
@@hyperduality2838 Einstein and Hawking are weak not only in terms of philosophy but also they are not important in physics. They are just famous. Hawking changed his 'thoughts' in every 3-5 years to sell his insignificant books. Continuity in physical tought along history of physics can be maintained without Einstein. He just combined little pieces of ideas circulating among his era's academia. It is very sad and scary, people are aware of nothing. Only being magazinal counts. When small people have long shadows, we approach to sun set
@@emmpati "Imagination is more important then knowledge" -- Einstein.
"Through imagination and reason we turn experience into foresight (prediction)" -- Spinoza describing syntropy.
The act of creating (emergence, synthesis, imagination) is a syntropic process.
Creation is dual to destruction, annihilation.
The one is defined in terms of the other.
Antinomy (duality) is two truths that contradict each other -- Immanuel Kant.
Increasing entropy causes you to update your predictions (syntropy) about the world around you and physicists make predictions all the time.
Absolute truth is dual to relative truth -- Hume's fork.
Thesis is dual to anti-thesis -- the Hegelian dialectic.
Being is dual to non being creates becoming -- Plato.
Duality leads to new laws of physics!
I bet I knew what you were thinking the moment after you said phi applied to x times phi... when you paused very slightly. .
You talk way too fast. This is great for those who already have a grasp of the material, but for teaching new concepts.
But was it a good place to stop? 🫠