What would be the result of the following divisions?
a. 1/0
b. 1/INFINITY
c. INFINITY/0
d. 0/INFINITY
e. INFINITY/1
f. INFINITY/INFINITY
g. 0/0
depending on what course you are taking, you can use limits to solve most of these, but if not, you simply say they do not exist.
a. 1/0 Divide by 0, does not exist
b. 1/INFINITY does not exist
c. INFINITY/0 divide by 0, does not exist
d. 0/INFINITY = 0 (0 divided by anything is 0)
e. INFINITY/1 = INFINITY (dividing in 1 piece is just itself)
f. INFINITY/INFINITY = 1 (x/x is always 1)
g. 0/0 = divide by 0, does not exist
a.) 1/0 = infinity (any positive real number divided by zero is infinity)
b.) 1/infinity = 0 (any real number divided by infinity is zero)
c.) infinity/0 = infinity
say, infinity = r/0, where r = a positive real number
so... (r/0) / 0 = r / (0*0) = infinity
d.) 0/infinity = 0
0 / (r/0) = (0 * 0)/r = 0
e.) infinity/1 = infinity
(Divide infinity by any positive number and you obtain infinity. Divide infinity by any negative number and you obtain negative infinity.)
f.) infinity/infinity = indeterminate
say, infinity in the numerator = r/0. denominator = s/0, wherein s = a positive real number
so... (r / 0) / (s / 0) = r/s
But what is r/s? It can be any rational number. So the answer is indeterminate.
g.) 0/0 = indeterminate
say, numerator = r*0, denominator = s*0
so... (r*0) / (s*0) = r/s
Again, r/s can be any rational number. Hence, indeterminate.
I saw this site (Math Forum - Ask Dr. Math) just now, and it has an interesting bunch of operations involving infinity and zero.