just perfect! i don't even know how to describe these explanations, no comments! Well done! Thanks a lot! I have not seen these kinda explanations for the graph theory.
If you have n nodes, create a list with size n. Every item is another list, containing the index of what nodes it's connected to. If you want weights, every item of that list must be a pair (index, weight). That's a representation called adjacency list.
If you shrink the map with the bridges down and use an electron , then it can pass all 7 bridges once. In fact it can pass them all at the same time. A human can do this also but a human's wavelength is small about 10^-32 meters. So there is a very small probability to cross all 7 bridges one time. You have to get out of Newtons classical world (which is an incorrect model) and think in terms of waves of quantum mechanics. The best example is the double slit whereby on electron passes through two slits in a barrier. So one electron would have no problem crossing two bridges in Königsberg at the same time. Thus the 7 bridge problem is solved and it is possible to cross all 7 just one time.
@@PowerUpStudio_Newtonian mechanics are not correct but they are an approximation so good enough. Now Math is exact , you deal in infinities and zero. There is no room for approximations. I can set up a similar problem to the 7 bridges with small particles and as you get the whole thing smaller, then you can do things like crossing 7 bridges all at the same time. Then you can scale it up and the probabilities of a human doing this are extremely small but not zero. Math has no room for "almost." Is 1+1 almost 2 ? or is it exactly 2? Math theories are built on elimination of possibilities by dropping things to zero , exactly zero or getting infinity and eliminating other possibilities. Integral calculus and derivative depend on things dropping to zero. The incompleteness theorems of Godel and Turing machines all work when you can get exactly zero or infinity. The Cantor diagonal slash depends on infinity working and 1 divide by infinity is zero. Math is full of theories that use the Newtonian mind model. The mathematicians think like Newton. Particles are solid and infinitely small. Its all wrong. So we end up with a bunch of math theories that all depend on one another. Some are useful. But what have we actually got ? What is it ? It seems to me that math is just an extension of Newtons world using Newtons physics.
I don't know why people don't use the real world , which is quantum. Why use Newtons world with h Plank's constant set to zero when it is wrong ? The 7 bridge problem is easy to solve with quantum mechanics and it is possible to cross all 7 bridges one time.
You can walk through each bridge once, if you can swim!
I appreciated the connection to social media, we really are all just nodes.
Sir taking infinity respect for sharing your great knowledge...we are so much great full to you
just perfect! i don't even know how to describe these explanations, no comments! Well done! Thanks a lot! I have not seen these kinda explanations for the graph theory.
Thank you!!
excellent quality very underrated channel
I really thank u
I have an exam of this graph theories tomorrow and u helped me to figure out what is going on
Amazing, technology merge with lessons.
Seems interesting! Keep em coming! Love your videos!
The bridge problem was also what started the donut=coffee mug madness called topology.
Great video! I hadn't seen the relation between graphs and multisets until today. Is there a book with this approximation?
if you are interested professionally to the discrete math, i suggest you "discrete mathematics and its applications" from Kenneth H. Rosen
Brilliant ❤️❤️
Sir please make video on Real Analysis
Sir You are one of the best teacher I have ever seen, please make videos on Real Analysis and Group Theory
Should I watch entire playlist as someone who is trying to become a self learned programmer
yes
@@yousefabdelgaber7498 100% yes. This is an amazing series.
When describing the graph with 1, 2, 3, 4, you missed an E...why didnt you connect (1, 3) ?? You seem to not have listed some connections at all.
How do you represent a graph on a computer?
If you have n nodes, create a list with size n. Every item is another list, containing the index of what nodes it's connected to. If you want weights, every item of that list must be a pair (index, weight). That's a representation called adjacency list.
If you shrink the map with the bridges down and use an electron , then it can pass all 7 bridges once. In fact it can pass them all at the same time. A human can do this also but a human's wavelength is small about 10^-32 meters. So there is a very small probability to cross all 7 bridges one time. You have to get out of Newtons classical world (which is an incorrect model) and think in terms of waves of quantum mechanics. The best example is the double slit whereby on electron passes through two slits in a barrier. So one electron would have no problem crossing two bridges in Königsberg at the same time. Thus the 7 bridge problem is solved and it is possible to cross all 7 just one time.
bruh were talking bout humans here and newtons mechanics are correct theyre just an approximation and still useful for most real world scenarios
@@PowerUpStudio_Newtonian mechanics are not correct but they are an approximation so good enough. Now Math is exact , you deal in infinities and zero. There is no room for approximations. I can set up a similar problem to the 7 bridges with small particles and as you get the whole thing smaller, then you can do things like crossing 7 bridges all at the same time. Then you can scale it up and the probabilities of a human doing this are extremely small but not zero. Math has no room for "almost." Is 1+1 almost 2 ? or is it exactly 2? Math theories are built on elimination of possibilities by dropping things to zero , exactly zero or getting infinity and eliminating other possibilities. Integral calculus and derivative depend on things dropping to zero. The incompleteness theorems of Godel and Turing machines all work when you can get exactly zero or infinity. The Cantor diagonal slash depends on infinity working and 1 divide by infinity is zero.
Math is full of theories that use the Newtonian mind model. The mathematicians think like Newton. Particles are solid and infinitely small. Its all wrong. So we end up with a bunch of math theories that all depend on one another. Some are useful. But what have we actually got ? What is it ? It seems to me that math is just an extension of Newtons world using Newtons physics.
Yayy 😊😊
I don't know why people don't use the real world , which is quantum. Why use Newtons world with h Plank's constant set to zero when it is wrong ? The 7 bridge problem is easy to solve with quantum mechanics and it is possible to cross all 7 bridges one time.
bruh 💀💀💀