<jupyter_start><jupyter_text>`3.101` and `3.118` are in fact equal. We can verify `3.102` as well.<jupyter_code>def p_r3_given_3(p, q, eps, delta):
    return p + (1 + eps + delta)*(p*eps - q*delta)
p_r3_given_3(p, q, eps, delta)
p_rk_given_c_derived(p, q, eps, delta, 3)<jupyter_output><empty_output><jupyter_text>Once again they are in fact equivalent! What is interesting is that there may in fact be no simple way to simplify `3.118` into the form expressed by `3.101` and `3.102`. However, they are functionally equivalent and yield the same answer. This could be explored more given the time.<jupyter_code>0.3 ** 100<jupyter_output><empty_output>
StarcoderdataJupyterStructuredCleanDedup