# A math expression I can't think a solution for

#### Mammoth

##### macrumors 6502a
Original poster

Okay, for this equation/expression to be solved at all, we must adhere to 2 rules/assumptions:

1. Infinity (∞) is never ending and does not stop under any circumstances
2. Subtracting anything from itself always equals zero

Now for the equation that I can't solve:
∞-∞=x
Solve for x.

Now it may seem with rule 2 that the answer is zero. But rule 1 says that ∞ is never ending, no matter what is taken away. Even though you are taking away infinity from itself, it is still infinity because it never ends.

Now that you see what I am thinking about this, you can see what I am thinking that could be an explanation:

1. ∞ is not a number thus rule 2 does not apply
2. Taking ∞ away from ∞ equals zero because rule 2 applies no matter how high the number

Sorry if this is confusing, I'm cobbling this together as I type, hence the potential confusion.

...So can it be explained? #### sammich

##### macrumors 601
x = ∞

Why? my guess:

We can say: ∞ is "some unfathomably large number" and '∞' does not equal '∞'.

∞(1) = k * ∞(2) where 'k' is any number.

So: ∞(1) - ∞(2) does not necessarily equal 0.

#### Mammoth

##### macrumors 6502a
Original poster
Good article. And here's the answer:

The short answer is --Anything you wish.
So I guess that means..

∞-∞=∞+1

Which I guess couldn't make sense because (Again a rule that isn't official) any positive number that is subtracted from a greater positive number always yields an answer lesser than the greater number. Example:
a-b=c
a>b, a>c

#### FredAkbar

##### macrumors 6502a
From what I can see, the problem (no pun intended) is that you (or they, whoever wrote the problem, I suppose) are using infinity in an equation as if it were a number, while really it's just a concept, usually meaning "infinitely large." So by "infinity - infinity," perhaps what is really meant is "a really big number minus itself."

In math speak, it would be like, the limit (as n approaches infinity) of the expression (n - n). This limit is 0. As long as the two infinity symbols both correspond to the same number (it can't actually correspond to infinity itself, as this isn't a number at all), then the answer is always 0.

#### siurpeeman

##### macrumors 603
∞-∞=∞+1

Which I guess couldn't make sense because (Again a rule that isn't official) any positive number that is subtracted from a greater positive number always yields an answer lesser than the greater number. Example:
a-b=c
a>b, a>c
what's up with these rules? who says we have to deal with positive numbers? and who says a has to be greater than b?
a - b = c
c can most certainly be greater than a. and for the record, ∞ + 1 is still ∞.

#### After G

##### macrumors 68000

You all are just reading it the wrong way.

Then the equation should read as follows:

8
|
8
||
X

The answer should be easily computed afterwards. (the above was just my cracked up sense of humor; the answer really can be anything, because infinity can be different sizes.)

#### malenfant

##### macrumors member
∞ - ∞ = ∞

an easy way to demonstrate this:

say you have a hotel that contains an infinite number of hotel rooms, and each room has a number. each room has one person in it. the front desk calls all of the rooms that have an even room number, and asks everyone to leave, so now only the rooms with odd numbers have people in them. an infinite number of people have left the hotel (since there are an infinite number of rooms with even numbers), but there are still an infinite number of people in the hotel (since there are an infinite number of rooms with odd numbers). qed: ∞ - ∞ = ∞.

#### cube

##### Suspended
Infinity is not a number, and some infinite sets are bigger than others (aleph number, there's an infinite (countable) number of sizes).