What is the value of ∞/2 in extended real numbers?

  • Thread starter Thread starter shunyadragon
  • Start date Start date
AI Thread Summary
The value of ∞/2 is defined as ∞ in the context of extended real numbers. While some argue this is incorrect, they often apply conventional real number logic, which does not account for the unique properties of infinity. In extended number systems, infinity behaves differently, and halving infinity still results in infinity. The discussion emphasizes that infinity remains constant, regardless of operations performed on it. Thus, ∞/2=∞ is logically consistent within the framework of extended real numbers.
shunyadragon
Messages
21
Reaction score
0
∞/2= ∞

Please comment. I do not thnk this is right.
 
Mathematics news on Phys.org
What number system are you working in? Strictly speaking, in the real number system, there is no "\infty" but you can think of that as "shorthand" for \lim_{x\to\infty} x/2. In that case, yes, that limit is \infty.

And, in any number system in which \infty is defined as a number (extended reals, for example) it is true that \infty/ 2= \infty.
 
Is there any logical or math problem with the value of ∞ in this question? Does the value of ∞ change?
 
shunyadragon said:
∞/2= ∞

Please comment. I do not thnk this is right.

Why not? What would you expect a never ending number which is halved to be?
 
shunyadragon said:
Does the value of ∞ change?
No. ∞ = ∞. Why do you think ∞/2 should have a different value from ∞?

(my assumption for this post: we are working in the extended real numbers or projective real numbers)

Most likely answer: you are trying to apply your intuition about algebra of real numbers. But ∞ isn't a member of the real numbers, and so it can behave differently -- and this particular algebraic behavior is one example of that different behavior.

If you actually think about what ∞ is defined to be or what sorts of things it can quantify ∞=∞/2 should actually be rather obviously true.
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Similar threads

I Formal definition of multiplication for real and complex numbers
Replies
2
Views
2K
I Post your favorite real analysis problem
Replies
5
Views
2K
I On base-b expansion of nonnegative reals
Replies
7
Views
2K
What are extended real numbers
Replies
1
Views
3K
B Arithmetic and our place value system
Replies
6
Views
108
I Zero raised to a positive real number
Replies
12
Views
2K
MHB How can we determine the sum of roots in a quadratic equation with real roots?
Replies
4
Views
2K
I Proof of a fact about real numbers - transcendental and algebraic
Replies
7
Views
1K
MHB Min Value of $a^2+b^2$ in Quadratic Equation
Replies
1
Views
1K
I Newton-Raphson Method With Complex Numbers
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top