9 Matching Annotations
  1. Aug 2023
    1. one early reader of this write-up decided to use half 3x5 cards, so that they’d fit in mtg deck boxes.

      First reference I've seen for someone suggesting using half size 3 x 5" index cards so that they could use commercially available Magic: The Gathering (MTG) boxes.

      Oxford and possibly other manufacturers already make 1/2 size 3 x 5" index cards.

  2. Apr 2023
    1. 5
    2. subspaces of a normed spaceX (of any dimension)

      I just discovered that the subspaces in vector spaces are very different compare to metric spaces.

      1. A subspace of a metric space just have to be a metric space.
      2. A subspace of a vector space will still have to retain the vector space structure. But if it's viewed as a metric space, this doesn't have to be the case.

      Also take note that this is talking about any spaces of dimensions.

    3. 2.5-6 Theorem (Continuous mapping)

      Continuous mapping preserves compactness in finite dimensional spaces.

    4. 2.5-5 Theorem (Finite dimension)

      Compact Closed unit ball in a normed spaces would mean that we have finite dimension.

    5. 2.5-4 F. Riesz's Lemma

      Riesz's Lemma, preparing for a theorem about the norm ball in finite dimensional spaces.

    6. 2.5-2 Lemma (Compactness)
    7. 2.5-1 Definition (Compactness)



  3. Jul 2022