if infinite/infinite=1,does it follow that 0/0=1-to me the two statements are undefined?so much for man-made x

Answer 1

I agree with the first two answers. Infinity/Infinity is undefined. To define such a relationship you need to say something like

x/x

and then say as x tends towards infinity x/x =1. But x/x =1 anyway so your statement has no meaning.

If you said Y=(1+x)/x then you could say that as x tends towards infinity Y tends towards 1. However, Y never equals 1 except in the limit where x=infinity.

Similarly x/x =1. However, as x approaches zero there is a singularity which would occur if you drew a graph of x/x against x. It would be a straight line at f(x)=1 until x=0 when it would be undefined.

You can define it if you want, but there is really no point as it serves no purpose.

Answer 2

The symbol for infinity is the 8 rotated 270 degrees.

That 00 you speak of could be the 8 turned 270 degrees

My avatar image shows you this symbol, plus it will show you inifinity as you say above, but you haven't quite given it all.

Its like this....1001
Because of reflection
Understanding how 0 creates a one gives you the answer of infinity because as the 0 was created it created the 1=one rotation of the zero creates one rotation therefor a 1 was made exactly the same time as the 0. 0 as a number means nothing therefore the 1 is greater and will stand before the 0 and with reflection and opposites brought in we have 1001
11 dimensions there, see it?
Hmmm, or is it a 2. Or is it astrology and November and February working opposite sides of a chart? Sounds like my time charts shared in my 360 too
Light and dark. Two parrallel worlds of awake and sleep, or light and dark, or 11 dimensions because remember the 2x0=0 as numbers yet continuance

If you look at my avatar, you will see the infinity symbol of the 8 rotated 270 degrees to give us 2x0 together. My avatar shows us there are 8x8=64=10...

Much more explained in my 360 too

Answer 3

This is my seventh attempt at trying to answer this question. I'm not saying loads of other people have asked it before, I mean that I keep deleting what I've written. So here goes, seventh time lucky.

You have chosen two undefined 'numbers' for your statements, but your undefined 'numbers' have similar properties. It's true, that your statements will therefore be undefined, as two times zero can equal zero, so therefore it follows that it's possible for zero to be divided by zero and equal two. It could also equal four million, three hundred and eighty-seven thousand, two hundred and six. That's what makes it undefined. However, if you are presuming that infinite/infinte is one, then, because of their similar mathematical properties, it follows that zero/zero should also equal one.

Sometimes you have to make a presumption in order to make a rule work, because for every rule there is one exception. And the exception to that rule is that sometimes there are two.

In this case there are two. However I thought this was why we have those stupid symbols to put next to statements like these, such as the weird R sign to show the statement only works for real numbers. Maybe, for your statement to be defined, it requires one of those symbols to say what it works for.

Answer 4

Hey.

I have read some of the answers and perhaps Im misunderstanding your question. I think that you are asking about limits and not about infinit sets, and their cardinality

By the way, Doug is right.

Infinite/infinite can have any result

Example: lim x^3/x^6 is 0 when x tends to +oo
lim x^6/x^3 = +oo
lim 2x^3 / 6 x^3 = 1/3
etc

So: you have to compare infinities.

Lets now see what happens to the functions who tend to 0

lim x^3 / x^6 when x tends to 0 is +oo.
lim x^6 / x^3 i 0
And lim 5x^2/7x^2 = 5/7

So, you may have any kind of result in both cases.

Ana

Answer 5

I hate to say it, but SAN really doesn't have a clue.

If X is the set of all even integers, and Y is the set of *all* integers (even and odd) then let f(z) = 2n take Y -> X clearly 'matches up' all of the even integers with all of the integers since for every y ε Y there is one and only one
x ε X such that 2y = x. Likewise if f^(-1) = n/2 takes X -> Y then clearly for all x ε X there is one and only one y ε Y such that x/2 = y and thus the two sets must have the same cardinality.

It's refered to as a 'countable infinity' (or infinity of order 'aleph nought') It is also the cardinality of the rationals (which Cantor proved over 100 years ago)

But the irrationals are a different beast and they're called an 'uncountable infinity'.


Doug

Answer 6

Any entity divided by itself = 1. 0 is not a entity, it is a symbol representing the absence of an entity.

Asking how many nothings there are in a nothing is meaningless, and hence the value is undefined.

I hereby define 0/0 as the snoogin. Next time you need to write down 0/0, just write snoogin instead.

Answer 7

think out what the divide function does. It seperates the top part of the fraction into an equal number of parts. Thus 10 / 2 separates 10 (apples maybe) into 2 separate piles of 5 each.

The question infinty / infinity (or any number dividied by itself) is always going to be 1. It's exactly the same as dividing 10 into 10 equal piles of 1. We just have an infinate number of piles of 1.

We can not however divide by 0. You can not separate 10 apples into zero equal piles. Likewise dividing anything else by zero is meaningless.

Answer 8

0*3 = 0
0*6 = 0

whcih means 0/0 = 3
and 0/0 = 6

thus 0/0 can have practically all values

and thus it is undefined

same is the case with infinity.....

Answer 9

Slow down there pal

∞/∞ does not equal 1. It is undefined. So yes, both the equation you stated are undefined.

Hurray for the man-made x. Don't forget... all mathematics is "man made"

Answer 10

Actually, series analysis indicates some infinities are larger than others. For instance, the ratio of even integers to all integers is 1/2, while the ratio of integers to real numbers is zero.

Edit: NEVER MIND. Those dusty old neurons were obviously faulty. See Doug below.

clueless..