Practice problem
Which of the following are ways of defining the limit superior of a sequence? Select all that apply.
lim supn→∞xn:=limn→∞supm≥nxm\limsup_{n\to\infty}x_n := \lim_{n\to\infty}\sup_{m\geq n}x_mlimsupn→∞xn:=limn→∞supm≥nxm
lim supn→∞xn:=supn≥0supm≥nxm\limsup_{n\to\infty}x_n := \sup_{n\geq 0}\sup_{m\geq n}x_mlimsupn→∞xn:=supn≥0supm≥nxm
lim supn→∞xn:=infn≥0supm≥nxm\limsup_{n\to\infty}x_n := \inf_{n\geq 0}\sup_{m\geq n}x_mlimsupn→∞xn:=infn≥0supm≥nxm
lim supn→∞xn:=supn≥0infm≥nxm\limsup_{n\to\infty}x_n := \sup_{n\geq 0}\inf_{m\geq n}x_mlimsupn→∞xn:=supn≥0infm≥nxm
Type a concept, like “slope” or “photosynthesis”.