what is left if you substract infinite from infinite for infinite times?

Answer 1

It depends. :) You first need to clarify the question. Let's say that an object (e.g. a "number") has the value infinity if it is has a bigger (or equal) value than any other comparable object. For instance, if we're comparing numbers, then we would say that a number is infinity if it's bigger than or equal to any other number.

Let's think about some concrete examples.

1. The sequence 1, 2, 3, 4, ... is eventually infinite. This is because, given any number, there is a term in the sequence that is bigger than or equal to the given number. So, according to our definition of infinity, the terms of the sequence "tend to infinity". Let's denote this sequence by (n).

2. Similarly, the sequence 1, 4, 9, 16, ... "limits" to infinity. Denote this sequence by (n^2).

What is "infinity minus infinity". Well, it depends:

(n) - (n) = 0
(n^2) - (n) = "infinity"

Worse, consider

3. the sequence 2, 3, 4, 5, ... Denote this by (n+1).

Now, infinity minus infinity = (n+1) - (n) = 1.

Okay, but you asked about "infinity minus and infinite number of infinities". To see that the answer is a resounding "it depends on the situation", consider

4. the sequence 1, 4, 27, 256, ... denote this by (n^n)

and

5. the sequence 1, 16, 27^3, 256^4, ... denote this by (n^n^n)

now consider "infinity minus and infinite number of infinities" in the cases of

(n^n) - (n) - (n) - (n) -.... = 0

and

(n^n^n) - (n) - (n) -(n) -... = infinity

Answer 2

The question is not specified well enough. It depends on the situation. Infinite what? An infinite set? An infinite number?

In case of numbers, if you extend the real numbers with the symbols -infinity and infinity then the operation infinity-infinity is usually left undefined, thus the question makes no sense: you cannot subtract infinity from infinity even one time.

If you talk about infinite sets, e.g. the real numbers, then depending on what you subtract, the remaining part may be both finite and infinite.

For example, if you subtract intervals of the type [n,n+1] (where n is an integer) from the set of reals infinitely many times, you can reach the empty set.

However, if you only subtract all rationals in the intervals of the type [n,n+1] (where n is an integer) from the set of reals infinitely many times, you will reach something that is still infinite (and in some sense, the remaining set, which is the set of irrational numbers, will have the same "number" of elements as the original set of reals!).

Many people ask questions about infinity here. Study calculus and set theory if you are interested in infinity. Otherwise it is all speculations and science fiction.

Answer 3

The problem with your question is that infinity isn't a number; it's a trend. "infinity minus infinity" makes absolutely no sense, because you're using the term "infinity" like it's a real number. But it's not.

In Calculus, the *concept* of taking infinity minus infinity is there, but you aren't actually doing so (because limits involved approximations anyway, i.e. things are *approximately* equal to infinity).

Instead of infinity, had you said "a really big number", then that's what limits are based off of. What is left if you subtract a really bi number from a really big number, a really big number of times? That answer can range from some value, or a really big number.

Answer 4

Admit you just wanted to waste five points. Admit it. C'mon. You couldn't even spell infinity correctly. Admit it. C'mon.

Answer 5

Infinity is not a number...it is a concept!!

Answer 6

It sounds originally but give no sense. ;-)