What is infinity - 1 and the square root of that?

Question

Clue: use surreal numbers

Answer 1

In most math classses, infinity - 1 is still infinity, and so is the square root of that. But John H. Conway came up with a number system in which you can subtract 1 from infinity. He calls infinity w (actually omega, but I am using the closest Latin letter), and can be thought of as the set of all the natural numbers {0, 1, 2, ...}. Infinity - 1 is then the first infinite number that is "created" after w and less than it. You get a downward sequence of numbers w, w-1, w-2, ... and the first number created between {0,1,2, ...} and {w, w-1, w-2, ...} is w/2, or half of infinity. In this way Conway defines addition and multiplication for all these infinite numbers; indeed one can take the square root of w-1 in his system. This system of numbers is now called the Surreal Numbers.

Answer 2

Since infinity doesn't end- goes on and on- it isn't a real number. A million, a trillion, none compare to infinity because infinity is greater than those.
So if you can't pin point the number, assign it a value say x.
You would have X-1=Y. We can't find Y because we don't know X. Then you are looking for the square root of Y and I forgot how to show that but hopefully you get the point.
Now if I could give you a blackboard full of equations on how to prove or dis-prove this I would be at Harvard submitting my proof and not giving it to you over the internet.
LOL

Answer 3

Well infinity - 1 is still infinity.

And the square root of infinity is also infinity.

So the answer is infinity! Weird hey?

Answer 4

The answer is infinity.

Think about this. If you have an infinite number of apples and you eat one, you will still have an infinit number of apples. Another way to look at it is there are an infinite number of integers from 1 to infinity. There are also an infinite number of integers from 2 to infinity (I took away 1).

Answer 5

that question can't be answered simply because there are different levels of infinity. The limit as x approaches infinity of x^2 increases faster than the limit as x approaches infinity of log(x)... they both will reach infinity but which one will reach it faster? obviously x^2, so you can't answer the question because infinity is not a finite number and is more or less a variable if you think of it in the way I've described.

Answer 6

This question is about as useful as arguing over whether 0.999... = 1. It is not equal to 1. However, it makes no difference in any of our mathematics. As someone has already stated: infinity is not a number just as it makes no sense to say the 9s go on forever because forever is not defined.

Answer 7

the respond isn't 0 while x -> +inf, that's infinity. Edit : lim sq. root ( x^2 + a million) + x ) = 0 ..... your instructor is robust right here. x -> -infinity because of fact that lim suitable and left are no longer equivalent, lim does not exist while x attitude to infinity.

Answer 8

The above poster is correct:

infty + a = infty
infty * a = infty
infty^a = infty

where a is any constant what so ever that is non-infinite. You don't get away from this until you start doing things like:

infty^infty

This expression creates another class of numbers called transfinite cardinal numbers.

Answer 9

infinity minus anything (excpet infinty) will always equal infinity! the square root of infinity is still infinity

Answer 10

Considering that 'Infinity' has no numerical value, your question is moot.