Concept of Infinity?

Question

Just a real sort question...

Is it possible for a number to actually be infinity and if not, wouldn't saying a number is infinity actually mean it is approaching infinity?

So is saying a number is infinity mean it approaches infinity?

I see... Thanks bud.

Answer 1

No, you can't actually treat infinity as a real number, because it leads to contradictions. For example, what is infinity plus 1? Infinity? That means x = x + 1 for some value of x, which means when you subtract x from both sides 0 = 1.

Using limits is a way to get around this problem. You can say that 1/n approaches 0 as n approaches infinity. But strictly speaking you can't "plug in infinity for n". Or similarly, 1/n approaches infinity (or rather "grows without bound") as n approaches 0. But as a rule in math you can't divide by zero, because again this leads to contradictions. If 5/0 equals some number x, then 5 = 0*x, which can't happen.

Strangely enough, you can have different "classes" of "infinity". Graduate classes in Real Analysis teach that you can have "countable infinity", where an infinite set of objects can be put in 1-to-1 correspondence with the cardinal numbers, and "uncountable infinity" where they can't. It turns out, for example, that although there are an infinite amount of values between 0 and 1, there are "countable" infinity number of rationals but an "uncountable" number of irrationals. Cantor was one of the leading mathematicians in this field. You can search for his stuff on-line.

Answer 2

No it is not possible for a number to be infinity.

Infinity is a concept. The main reason the concept is needed is to understand the set of real numbers. Real numbers don't just go from -1000000 to 1000000. They go on forever in both directions. We call the symbolic endpoints of this "number line" negative infinity and positive infinity.

I like to compare the idea of infinity to time and space. If you can understand the concept of infinity, you can understand the theories of infinite time and space (theories which I firmly believe to be true). That is, time and space are both infinite - there was no beginning to time and there will be no end, and there is no beginning nor end to space. These concepts are very difficult to grasp for most people simply because humans naturally like to think in finite terms.

As for the meaning of "approaching infinity"... We say "approach infinity" just as we say "approach 0" (or any other real number). It simply means "as it gets closer and closer to". In the case of approaching infinity you could say "as something gets larger and larger". The difference between approaching infinity and approaching a real number is that while you can actually reach a real number, you can only approach infinity, since it is only a concept.

Answer 3

Infinity is not a particular value; you could always add something to a particular value.
Approaching infinity is a better expression.
Saying a number is infinity doesn't actually mean it is approaching infinity

For instance
The value of 1/x approaches infinity as x approaches 0

Answer 4

To say that something approaches infinity gives a wrong idea. The correct terminology is to say that something increases (or decreases) without bound. It means that the number sought can never be attained.

Answer 5

A definite number cannot be infinite. That is a self-contradiction!

Any number divided by zero would result in Infinity.

A number divided by x approaches infinity as x tends to zero.

Answer 6

Infinity is a nonreal number. Therefore, when it is said that a value F(x) "is" infinite, a truer statement would be that as x is approached F(x) becomes increasingly greater in magnitude.

(this is the same as your second assumption)