I'm a mathematician at the Ohio State University. I make math videos. I've posted lectures for my Coursera courses, Calculus One and Calculus Two: Sequences and Series. I'm currently working on a new MOOC on multivariable calculus and linear algebra.
You can find out more on my homepage at kisonecat.com/
If the example is taken by you is of alternating series i.e., the series (-1)^n (n/n+1) is converge or diverge? Can this alternating series is converge because limit n tends to 1(not equals to 0).
Jim Fowler my dude, i just bought a laptop from a third party and noticed that the OneDrive of the laptop is already full, i went to check and somehow the it was filled with your videos, 189 of them but all dated to 1st of January 1970. I don't know if the previous owner of this laptop is a huge fan of yours but i accidentally found your channel from the intro and the name MOOCulus.
I know this was made about 7 years ago, but I still want to provide a quick proof by contradiction for why if A is not invertible, then AB is not invertible: Let AB be invertible. Then, there exists such a matrix C that when multiplied with AB yields the identity matrix, I. We can write this as an equation: AB * C = I Now through associative property of matrices, we find A * BC = I So if AB is invertible, A must be invertible as well. Therefore when A is not invertible, AB must be not invertible as well.
Unless otherwise stated it should essentially be done away with as a “symbol” of an “operator” on the equation that comes after it to instruct the mathematician to take the derivative of the equation with respect to the bottom variable (x,y,x,s,t,u,v,etc)
It’s best interpreted as if an epsilon change is made on another axis how much does the axis in question change but until a much higher level is needed it should just be viewed as notation for the current base along that axis to quantify the units.
Let X={a,b,c} and ~ be {(b,b), (b,c), (c,b), (c,c)}. This example is symmetric and transitive but not reflexive. I like having a non-vacuous example as well.
Thank you so much for explaining this to me.I used to think that 0.9 repeating does not equals 1, because it does not feel like it intuitively.Haven't thought of using infinite sum to prove this
thank you! this is the only one video I found which really helped me; what you say here seems so fundamental and it is really difficult to find a neat explanation of it! it seems mathematicians and engineers nowadays worry only about applications, and they have lost intuition and can't explain even the most fundamental things conceptually;
the pauses sure are creepy.. must be the hardware video encoding, not the interpreted language with recursively defined arithmetic. like the idris dev advertising his 86000 line program compiling in under 4 minutes. btw what is your genetic background? fowler strikes me as an unusual name for the physiognomy.
