5 Matching Annotations
  1. Nov 2023
  2. Mar 2021
  3. Feb 2021
    1. For instance, the polynomial function on RR\mathbb{R} defined by f(x)=x2f(x)=x2f(x) = x^2 is not a homomorphism of rings

      \( r_{1} = 1, r_{2} = -1 \)

      \( e_{r_{1}}(f(x)) + e_{r_{2}}(f(x))\\= f(r_{1}) + f(r_{2})\\= f(1) + f(-1)\\= 1+1\\=2 \)

      However...

      \( f(r_{1} + r_{2})\\= f(1 + (-1))\\= f(0)\\= 0 \)

      ...and...

      \( 2 != 0 \)

  4. Nov 2020
    1. space complexity is O(n2n)On2n<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:mi>O</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>n</mml:mi><mml:msup><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:mfenced></mml:math>.

      wait I thought it was the same as the time complexity

  5. Oct 2020