Dear friends ! Thank you for watching. Please consider subscribing and sharing the video. If you liked the video and wish to buy me a coffee you can do it here: www.buymeacoffee.com/mathphysicK Link to the video with the visual proof of Cantors Lemma: ua-cam.com/video/ijMvFprZqbU/v-deo.html&ab_channel=Math%2CPhysics%2CEngineering
Dear Friends the proof of Cantors lemma that is used in this video can be found in the playlist. For your convinience I add the link to the video in this comment: ua-cam.com/video/ijMvFprZqbU/v-deo.html&ab_channel=MathPhysicsEngineering
A slight issue in the example open cover {U_n}_n=2^\inf if n=2 it will be the interval (1/2,1/2) which is not an open interval (defn: the open interval (x,y)={z: x
Thank you for your comment! Technically this is fine because the empty set is always considered to be open. In the definition of a topology on a set X, the set X and the empty set are open acording to definition. It is also open according to the definition in the slides since for every point in the set (of which there are none) the open ball around such a point is contained in the set. It is ok according to the logical implication of A=>B, so if A is false , A=>B is always true no mater what is B.
Dear friends ! Thank you for watching. Please consider subscribing and sharing the video.
If you liked the video and wish to buy me a coffee you can do it here: www.buymeacoffee.com/mathphysicK
Link to the video with the visual proof of Cantors Lemma:
ua-cam.com/video/ijMvFprZqbU/v-deo.html&ab_channel=Math%2CPhysics%2CEngineering
Amazing proof!
Dear Friends the proof of Cantors lemma that is used in this video can be found in the playlist. For your convinience I add the link to the video in this comment:
ua-cam.com/video/ijMvFprZqbU/v-deo.html&ab_channel=MathPhysicsEngineering
Apologies for the low sound quality, the microphone was on its highest volume setting. :(
A slight issue in the example open cover {U_n}_n=2^\inf if n=2 it will be the interval (1/2,1/2) which is not an open interval (defn: the open interval (x,y)={z: x
Thank you for your comment! Technically this is fine because
the empty set is always considered to be open. In the definition of a topology on a set X, the set X and the empty set are open acording to definition.
It is also open according to the definition in the slides since for every point in the set (of which there are none)
the open ball around such a point is contained in the set. It is ok according to the logical implication of A=>B, so if A is false , A=>B is always true no mater what is B.