Subtracting any finite quantity from an infinite quantity

[Nick666]

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

 

[Kummer]

What is that supposed to mean?

 

[Nick666]

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

Ok, too simple maybe. Replace apples with time.

 

[VietDao29]

If you substract a finite amount of apples from an infinite amount of apples, what's the result?

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

Infinite amount of apples ?

Well, you are closed, it's negative infinity: $$a - \infty = - \infty , \ \ \ \mbox{where } a \neq \infty$$

Ok, too simple maybe. Replace apples with time.

Err, not sure what you mean here. =.="

 

[arunbg]

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

 

[Nick666]

Including time?

The other way around vietdao.

 

[arunbg]

Well, what's the difference with time?

 

[Nick666]

Dont know ...just asking.

So let's say a thing has been there forever, a dog for example.

That would mean he`s 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. ... ?

 

[HallsofIvy]

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.

 

[arunbg]

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

 

[Nick666]

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

Yeah, that's exactly what I`m thinking about.

But am I wrong in my assumptions cause of the fact that I can't say there`s infinite time? Infinite time doesn't 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?

 

[arunbg]

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?

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.

 

[Nick666]

Well, replace create with add.

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

 

[HallsofIvy]

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.