our lecturer left all these theories to us and he just ignore them ,also the textbook is just way too fancy to describe things...appreciated having you
Thank you for the video. Despite having a PhD in math, this was never something that I went through carefully. I had a student ask me about how to construct the integers from the naturals and was embarrassingly stumped (they emphasized constructing the reals to us in grad school but left out integers and rationals). This was a phenomenal crash course and now I can explain it to my student! Thank you!
Considering that Abstract Algebra I / 101 is a must have prerequisite: the creation of the Integers from the Naturals can't be explained more clearly than you did in this video lecture. ( It can even be done from my preferred definition of the Naturals: just 1, 2, 3, etc. ). Thanks!
I think of subtraction equivalence classes as "the space between numbers." So each class represents all possible forms of this same space. Anyways, just how I think about it.
Yo have any thoughts on the old Jesuit mathematicians, naturalists, scientists? The idea of an apostolic educational/missionary/scientific order which puts theory to action and bears much fruit-I find them inspirational. For example near me there’s a monument to a certain Jesuit math/logic professor (Carlos Spinola) who was martyred in Japan. Teaching math and training priests clandestine in the forests of Japan- enduring torture for beliefs in which there was no contradiction in theory and practice. The Jesuits synthesized that classical Euclid-Aristotle-Christian education and went to the ends of the Earth to preach it and die for it.
I may have missed it, but from the beginning of the video you use subtraction and later in the video while defining addition you set things up as a difference... Was subtraction actually defined anywhere? (I still thumbs'ed up the video- this series has been tremendously helpful!)
I think subtraction and its properties should have been defined and proved prior to defining integers at least for the sake of completion. Because thats the way we studied it at school and everything till now has been following that sequence. Buts thanks anyway for all these videos and giving me sense of closure.
our lecturer left all these theories to us and he just ignore them ,also the textbook is just way too fancy to describe things...appreciated having you
Thank you for the video. Despite having a PhD in math, this was never something that I went through carefully. I had a student ask me about how to construct the integers from the naturals and was embarrassingly stumped (they emphasized constructing the reals to us in grad school but left out integers and rationals). This was a phenomenal crash course and now I can explain it to my student! Thank you!
Considering that Abstract Algebra I / 101 is a must have prerequisite: the creation of the Integers from the Naturals can't be explained more clearly than you did in this video lecture. ( It can even be done from my preferred definition of the Naturals: just 1, 2, 3, etc. ). Thanks!
We can use also definition of positive integers in this partitions : y is member of x and for negative integers : y is not member of x .
I think of subtraction equivalence classes as "the space between numbers." So each class represents all possible forms of this same space. Anyways, just how I think about it.
Thank you , this video is astounding and crystal-clear.
More videos please
Yo have any thoughts on the old Jesuit mathematicians, naturalists, scientists? The idea of an apostolic educational/missionary/scientific order which puts theory to action and bears much fruit-I find them inspirational. For example near me there’s a monument to a certain Jesuit math/logic professor (Carlos Spinola) who was martyred in Japan. Teaching math and training priests clandestine in the forests of Japan- enduring torture for beliefs in which there was no contradiction in theory and practice. The Jesuits synthesized that classical Euclid-Aristotle-Christian education and went to the ends of the Earth to preach it and die for it.
thank u i luv u
Awesome explanation, thanks.
I may have missed it, but from the beginning of the video you use subtraction and later in the video while defining addition you set things up as a difference... Was subtraction actually defined anywhere? (I still thumbs'ed up the video- this series has been tremendously helpful!)
do you provide solutions to your exercises?
Thank you for the video, it was very clear explanation, very helpful :)
I think subtraction and its properties should have been defined and proved prior to defining integers at least for the sake of completion. Because thats the way we studied it at school and everything till now has been following that sequence. Buts thanks anyway for all these videos and giving me sense of closure.
@Boundary Theory Why is it impossible ?
Thanks very much it helped alot.