What is infinity minus infinity

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In summary, two users discuss the concept of infinity and its manipulation in mathematics. The first user asks about infinity minus infinity and the second user responds by explaining that it depends on the definition of infinity and that for most definitions, the result is undefined. The first user then clarifies that they mean infinity as a limit, to which the second user responds with an example of \lim_{x\to\infty} x-x being equal to zero. The conversation continues with further examples and explanations of limits and their relationship to infinity. The expert summarizer then interjects and provides a concise summary of the conversation, emphasizing the inability to define infinity minus infinity due to its potential to be anything.
  • #1
jontyjashan
68
0
hello
i m a new user
what is infinity minus infinity
 
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  • #2


Depends, what do you mean by infinity?
 
  • #3


its a limit
 
  • #4


There's really no good way to subtract 'infinity' from itself. For almost all definitions of infinity (there are lots!), the result is undefined.
 
  • #5


jontyjashan said:
its a limit

You mean [tex] \lim_{x \to \infty} x - x [/tex]? Then it's zero.
 
  • #6


if infinity minus infinity is zero then
infinity + 1 =infinity
infinity - infinty =1
0=1
 
  • #7


Please do not say that you mean one thing by "infinity" and then change in your response!

When asked, "What do you mean by infinity", you responded "its a limit" (which is pretty much meaningless) a dx responded to that with "If you mean [itex]\lim_{x\to \infty} x- x[/itex] then it is 0".

He did NOT say "infinity- infinity = 0". He was trying to respond to your vague answer.

He could as well have pointed out that [itex]\lim_{x\to \infty} x^2- x[/itex] is also "infinity minus infinity", in that [itex]lim_{x\to \infty}x^2= \infty[/itex] and [itex]\lim_{x\to \infty} x= \infty[/itex], and that limit is equal to infinity. In fact, given any number a, [itex]\lim_{x\to \infty} x+ a= \infty[/itex] and [itex]\lim_{x\to \infty}= \infty[/itex] so [itex]\lim_{x\to\infty}(x+a)- x[/itex] can be said to be "infinity - infinity" but that limit is obviously a. If, by "infinity" you mean "its a limit" then, depending on exactly which limit you use you can make "infinity - infinity" equal to anything.

What you need to understand is that when we talk about "[itex]\lim_{x\rightarrow \infty} f(x)[/itex] or [itex]\lim_{n\rightarrow\infty} a_n[/itex], that "infinity" is just short hand for "x (or n) increases without bound". Also saying that [itex]\lim_{x\rightarrow a} f(x)= \infty[/itex] or [itex]\lim_{n\rightarrow \infty} a_n= \infty[/itex] we are NOT saying that the limit is "the number infinity", we are saying that the limit does not exist in a particular way.

In many textbooks they will say, for example, that [itex]\lim_{x\to a} x^2[/itex] converges to [itex]a^2[/itex] but that [itex]\lim_{x\to 0} 1/x[/itex] diverges to infinity- that is, the limit does not exist.
 
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  • #8


jontyjashan said:
hello
hi

i m a new user
I can tell

what is infinity minus infinity
Doesn't exist for what I feel you define inf. as

Bye
 
Last edited:
  • #9


succinct!
 
  • #10


protonchain said:
hi
i can tell
Doesn't exist for what I feel you define inf. as
Bye

hahahahahahahahaha you are great. :biggrin:


but back to jontyjashan, the simple answer is that infinity minus infinity can not be defined, because it can be anything. it's like asking, what is anything divided by zero? it doesn't make sense to ask a question like that.
 
  • #11


dx said:
You mean [tex] \lim_{x \to \infty} x - x [/tex]? Then it's zero.

LOL!

That was the exact example I was thinking when I read his limit comment.
 

1. What is infinity minus infinity?

Infinity minus infinity is a mathematical expression that is undefined. It cannot be solved or given a numerical value.

2. Is infinity minus infinity equal to zero?

No, infinity minus infinity is not equal to zero. As mentioned before, it is an undefined expression and cannot be given a numerical value.

3. Why is infinity minus infinity undefined?

This is because infinity is not a number, it is a concept that represents something that is endless or boundless. Therefore, subtracting one form of infinity from another does not result in a finite number and is therefore undefined.

4. Can infinity be subtracted from infinity?

Yes, infinity can be subtracted from infinity, but the result will always be undefined. This is because infinity is not a precise value and cannot be manipulated like regular numbers.

5. How is infinity minus infinity different from other mathematical operations?

Unlike addition, subtraction, multiplication, and division, infinity minus infinity does not follow the usual rules of arithmetic. It is a special case that cannot be solved and must be represented as undefined.

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