# Subtracting any finite quantity from an infinite quantity

1. Jul 8, 2007

### Nick666

Between a finite amount of x and in infinite amount of x, is there an infinite amount of x ?

2. Jul 8, 2007

### Kummer

What is that supposed to mean?

3. Jul 8, 2007

### Nick666

If you substract a finite amount of apples from an infinite amount of apples, whats the result? Infinite amount of apples ?

Ok, too simple maybe. Replace apples with time.

Last edited: Jul 8, 2007
4. Jul 8, 2007

### VietDao29

You mean: $$a - \infty , \ \ \ \mbox{where } a \neq \infty$$. Right?

Well, you are closed, it's negative infinity: $$a - \infty = - \infty , \ \ \ \mbox{where } a \neq \infty$$
Err, not sure what you mean here. =.="

5. Jul 8, 2007

### arunbg

Subtracting any finite quantity from an infinite quantity, yields an infinite quantity. Such is the definition of infinity.

6. Jul 8, 2007

### Nick666

Including time?

The other way around vietdao.

7. Jul 8, 2007

### arunbg

Well, what's the difference with time?

8. Jul 8, 2007

### Nick666

Dont know ....just asking.

So lets say a thing has been there forever, a dog for example.

That would mean hes been there for an infinite amount of time.

If the dog creates something that is finite in time (a big poo, haha, maybe you see the analogies) it means that an infinite amount of time passed before he created the thing. ... ?

9. Jul 8, 2007

### HallsofIvy

Staff Emeritus
You are going to have to define your terms better. "Infinity" is not a member of the real numbers and ordinary arithmetic does not apply to it. There are a number of different ways of defining a system that includes all real numbers and "infinity". For most of those, I think $\infty- x= \infty$ for any real number x but I can't be certain about all.

As for "an infinite amount of apples" or "an infinite amount of time", as soon as you substitute a specific thing for "x", it stops being a mathematics question and becomes a physics question (maybe botany for apples?) and the answer would be that "an infinite amount of apples" or "an infinite amount of time" do not exist.

10. Jul 8, 2007

### arunbg

Echoing what Hallsofivy just said, there's no poo-poo time after infinite time

11. Jul 9, 2007

### Nick666

Yeah, thats exactly what Im thinking about.

But am I wrong in my assumptions cause of the fact that I cant say there`s infinite time? Infinite time doesnt exist? Why? Cant I assume it exists?

So, after all, if I assume infinite time exists, is it nonsense in a mathematical way, to say that something infinite in time created at some point something finite in time, right?

12. Jul 9, 2007

### arunbg

If you attribute no physical reality to time, I think your statement is equivalent to asking whether you can have an interval of finite numbers on an infinite number line. The answer is obviously yes.
However once you attribute ideas like "creating" a finite element from infinity, then you become vague. Again you will have to define these terms better.

13. Jul 12, 2007

### Nick666

Well, replace create with add.

How does one know he added a finite number to infinity, if the result is ...the same infinity ... ?

14. Jul 12, 2007

### HallsofIvy

Staff Emeritus
Are you talking about physics (time) or are you talking about mathematics? If you are talking about physical time, then, no, you can't just assume infinite time exists- either it does or it doesn't, there is no "assuming".

If you are talking about mathematics, then you should be aware that there are a number of different ways of defining "infinite"- you haven't defined how you are using the term.