Division Result

[cyberfish]

Divided by zero != divided by a number that APPROACHES zero.

I was referring to sth like 1/0, without limits.

[laserlight]

Same thing (or at least I meant by undefined what you mean by indeterminate).

From what I understand, undefined and indeterminate are two different concepts. Undefined means that the symbol or operation has no meaning, but indeterminate means that it can take some arbitrary value, depending on circumstances. In that sense, since 0/0 is indeterminate in mathematics, it is incorrect to say that "anything divided by zero is undefined".

[abachler]

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

a. 1/0 is unit infinity

b. zero

c. infinity/0 is infinity squared

d. 0/infinity is zero or technically zero squared since '0 divided by any number is zero'

e. Infinity /1 is still infinity

f. infinity / infinity is 1 as long as both are positive unit infinity

g. 0/0 is 1 since 0 / x = 0 * 1/ x and 1/0 = infiinty and multiplying a number by its recipricol is always 1 and also dividing any number by itself is always 1

remember that 5/0 != 4/0 and 1/0 != -1/0

[laserlight]

g. 0/0 is 1 since 0 / x = 0 * 1/ x and 1/0 = infiinty and multiplying a number by its recipricol is always 1 and also dividing any number by itself is always 1

By that same reasoning, 0/0 is 2 since 0 / x = 0 * 2/x. Consequently, if you do not call 0/0 indeterminate (or at least undefined), then we have a proof that 1=2, upon which it follows that 1=0. How do you address the statements made earlier in this thread concerning the undefined and indeterminate nature of the various expressions given in anirban's question?

[@nthony]

From what I can remember of calculus:
a. undefined (infinitely large)
b. undefined (infintely small)
c. undefined (infinitely large)
d. 0
e. infinity
f. 1
g. indeterminable

others of note are:
0^0 = 0 * 1/0 = indeterminate
0^infinity = 0
infinity^0 = infinity * 1/infinity = undefined
0 * infinity = undefined