If 1/0 = ∞ therefore ∞(0)=1 does this mean Nothing is impossible?

Question

If an infinite amount of nothing equates to something as in the above equation does this demonstrate that there has to be something rather than nothing in a cosmological context?

Answer 1

Go back to the rule. Any number multiplied by zero is zero.

Answer 2

What you really want to look at is 1/x as x approaches 0.
As x approaches 0, y becomes infinitly large.

This means for 1 = x*y you will find a combination of x*y that yields 1, even if x is veeeerrryyy small and y is veeeerrrry large but AT x = 0 this isn't true because it can't get there. The fuction y=1/x does not include x=0

When we equations like this that expresses things in the real world, typically, the nature of the system is only approximated by the equation and changes due to other variables. This may happen when something is quantized or other laws come into play. For example, the equation which expresses the discharging of a capacitor shows that as t approaches infinity the charge on the capacitor smoothly approaches zero. In all reality, that line probably doesn't become all that smooth if you zoom in on it due to the nature of the material used in the capacitor. It may very well maintain a small but constant charge that doesn't decrease with time.

So infinity*0 isn't = to 1.

Answer 3

People don't know math around here. In this context, 1/0 is not undefined because infinity is not a discrete number. Only in terms of a real number (a mathematical expression) is 1/0 undefined, and that's not what the questioner is asking. It's like saying "...you can't call the universe 'huge' because no one can precisely say exactly how big the universe is..." So what? "Huge" is not a discrete concept - I can't tell you the universe is 100 billion light years across, but I sure can describe it as huge.

So yes, 1/0 is infinity. 0/0 is indeterminate, but not x/0 where x is any number greater than zero. Only in the context of a discrete number is x/0 undefined.

And no, you cannot assign philosophical concepts to mathematical constructs. There's no logical basis.

Answer 4

Your equation in of itself is floored.

You have multiplied both sides by 0:

infinity x 0 = 0 (it does not equal 1)

1/0 x 0 = 0 (it does not equal 1)

You are trying to apply a mathematical principle which breaks down and cannot possibly be applied in this context.

It seems a simple enough conclusion, but when you study much more advanced maths (I have no idea how old you are, sorry), this is one of the little idiosyncrasies you will come to understand, and hopefully appreciate.

It may well be worth asking your maths teacher (if you are indeed in school as i suspect) to spend some time with you to explain where your equations break down.

Answer 5

I don't think my answer will add much to what has been said already, but I will try to express it in a different way.

As has already been said, infinity isn't a number.

When people say that '1/x tends to infinity as x tends to zero' this really means that you can make 1/x as large as you like by making x as small as you like. So if somebody says that the maximum value of 1/x is "some humungous number" you can prove them wrong just by making x a little bit smaller and just can always continue to do this.

So what you have in the second equation is Limit (1/x) as x->0 multiplied by 0.
Since zero is unaffected by the Limit operation you can rephrase this as:

limit[(0 x 1)/x] as x tends to zero = limit[0/x] as x tends to zero

Clearly 0/x is zero no matter how big x is.

So you have limit[0] as x tends to zero ... which is obvious ZERO.

The point is that you can't replace 1/0 by a symbol and treat that symbol like a number. What you have to do is go back to the operation that 1/0 represents.

Well maybe that is all as clear as mud, but I did my best.

Answer 6

Divide one by two. The answer is a half.

Divide one by one. The answer is one.

Divide one by a half. The answer is two.

Divide one by a quarter. The answer is four.

Divide one by a hundredth. The answer is one hundred.

As you divide by less, the answer gets bigger, so:

If y = 1 / x

then as x goes to zero, y goes to infinity.

We're not saying 1 / 0 = infinity. It is undefined. It is just saying that as x gets closer to zero, y gets closer to infinity.

And about the pie - It would take an infinite number of people to share the pie between in order for no one to get any. 1 / 0 is not 0

Answer 7

1/0 = ∞;
2/0 = ∞;
3/0 = ∞
etc.
Hence, ∞*0 = 1, ∞*0 = 2, ∞*0 = 3 etc.
Hence, ∞*0 is undefined, as it can be anything you like...
Draw your own conclusions.
Perhaps one possible conclusion is, "Nothing, is what you make of it", or multiply through both sides and get "Make the most that you can out of nothing."

Answer 8

The equation 1/0 = ∞ is not a valid equation, it is undefined. Therefore you cannot make the assumption above...

Answer 9

in an infinite universe not only is everything possible but it is also compulsory..famous quote by some famous person.....yes of course you are right except that zero or infinity are said to be 'a number tending to zero/infinity' which if you can get your head round is a very subtle differance...so if you wrote 1/(x>0)=(x

Answer 10

It's more interesting that they put 1 into nothing and came up with the universe. 0/1=the universe?

Answer 11

1/0 does not equal infinity. Its value is "undefined" which is not the same thing. That makes the second equation unhelpful. Anyway, what if your something or your nothing have imaginary components?