MF31: Parallelograms and affine combinations

[danyaikido]

Can we add points and vectors? What is the meaning of A (a point) plus v ( a vector) if they are different mathematical objects??

[njwildberger]

@danyaikido Yes they are different mathematical objects, but we are allowed to combine them as long as we do so clearly and unambiguously. It is like multiplying a vector by a number---they are different, but we can give meaning to the product as another vector. In the case of point plus vector, the result is intuitively natural; start at point A, move left by three units, end up at point B etc.

[danyaikido]

@njwildberger Thank you very much! Your approach to maths is very interesting. Do you have some video where you talk more about the real numbers? What about Dedekin's cuts or Cauchy sequences?

[njwildberger]

@danyaikido I discuss real numbers a little in Universal Hyperbolic Geometry 20. Dedekind cuts and Cauchy sequences are elaborate hoaxes, to be honest. They don't work, which is why you never see them laid out completely. I will bury them later in the MathFoundations series!

[chrishopf2010]

brain hurts