Now we just plug in x=0, and we see that zero to the zero is one! High School Teacher:Showing that approaches 1 as the positive value x gets arbitrarily close to zero does not prove that . The variable x having a value close to zero is different than it having a value of exactly zero. In words, that means that the value of is whatever approaches as the real number z gets smaller and smaller approaching the value x arbitrarily closely. Hence, if we do not use then the binomial theorem (as written) does not hold when a=0 because then does not equal .

When you want to outsmart the world, you turn to the facts. And the facts are in the science.