Theoritical Math questions about infinity and zero.?

Question

I was discussing the following with my bro. I have a point of view.....I would love to hear yours.
a) Infinity - Infintiy =
I am sure it is infinity, my bro thinks zero.
b) Infinity/Infinity =
We both agree on infinity
c) 0/0 = Undifined, zero, or One
I came across a math proof that used it as 1 once. So I am going with that.
Thanks in advance.

Answer 1

In the real number system, infinity is not considered to be one of the set of real numbers and so none of the operations are defined for it.

The notion of subtracting with infinity isn't really defined. You can't really do it, and if you could, the answer wouldn't mean much. The same applies to division by infinity.

Anything divided by zero is undefined, including zero.

Answer 2

Well the answers to your question are:

a) infinity

b) infinity

c) this is accepted to be an undefined form. It is not one. the reason the rate of multiplication and division are the same in this case as the same number is involved.

But in some cases where exponential function is involved the value of exponent determines the result because it is faster. That's when the answer 1 is possible for an expression resulting in 0/0

The best proof can perhaps be given if you try these in the calculator.

They all will result in error.

Answer 3

Any number subtracted from itself = zero inc. positive & negative numbers, so also includes infinity

Any number, apart from zero, divided by itself = 1, so infinity / infinity =1

You cannot divide any number by zero, so undefined.

Answer 4

all of the above are undefined. division by zero is not possible. while infinity is not a real no. so u cant add/divide with it...

Answer 5

a) Think of it this way:
for example
2n - (2n + 1) = 1 but if you let n --> inf then you get inf - inf = 1

But if you try 2n - 2n = 0 and let n--> inf then you get inf - inf = 0

yet another

let 3n - 2n = n then letting n-->inf gives

inf - inf = inf

So anything goes! This means that (inf - inf ) is an "UNDETERMINED" quantity



b) and c) are also undetermined quantiies and can be made to have any value we "wish"