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Orion1
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Is [tex]\infty - \infty = 0[/tex]?
Both square root of -1 and infinity can be rigorously defined as numbers; neither of them, however will lie on what we call the real number line (or more precisely, they are not "real numbers" in the technical meaning of "real").Anzas said:then why do we use arithmetic with complex numbers? they aren't really numbers after all
[tex]\sqrt{-1}[/tex] is not anymore defined than [tex]\infty[/tex]
Complex numbers are really numbers they just are an extention of the real number set and it's fairly easy to prove all the axioms that apply to the real numbers (except inequalities).Anzas said:then why do we use arithmetic with complex numbers? they aren't really numbers after all
[tex]\sqrt{-1}[/tex] is not anymore defined than [tex]\infty[/tex]
Anzas said:whats the definition of "number" i would say a number is anything that represents some kind of quantity but complex numbers do not they are more like a function than a number.
Look this up: http://en.wikipedia.org/wiki/NumberAnzas said:whats the definition of "number" i would say a number is anything that represents some kind of quantity but complex numbers do not they are more like a function than a number.
Zurtex said:Look this up: http://en.wikipedia.org/wiki/Number
The mathematical definition of a number does not have to have a physical representation, ever come across [itex]\pi^e[/itex] apples or -3 bricks?
No you don't, rather you owe the bank $25 and -$25 is used to represent this difference in direction of who owes who money, you can't actually take out this -$25 and show it to someone.whozum said:Well I do have -$25 in my account right now!
(Okay, this is also supposed to have a physicist and a biologist, but whatever!)
Infinity in cosmology
An intriguing question is whether actual infinity exists in our physical universe: Are there infinitely many stars? Does the universe have infinite volume? Does space "go on forever"? This is an important open question of cosmology. Note that the question of being infinite is logically separate from the question of having boundaries. The two-dimensional surface of the Earth, for example, is finite, yet has no edge. By walking/sailing/driving straight long enough, you'll return to the exact spot you started from. The universe, at least in principle, might have a similar topology; if you fly your spaceship straight ahead long enough, perhaps you would eventually revisit your starting point.
antinomies said:... I can see in space the possibility of any finite experience ... we recognise [the] essential infinity of space in its smallest part." "[Time] is infinite in the same sense as the three-dimensional space of sight and movement is infinite, even if in fact I can only see as far as the walls of my room."
antinomies said:... what is infinite about endlessness is only the endlessness itself.
Infinity - infinity is a mathematical operation that involves subtracting one infinite quantity from another infinite quantity.
Yes, in some cases, infinity - infinity can be equal to 0. However, this is not always the case and depends on the specific values of the two infinite quantities.
Infinity is not a finite number and therefore does not follow the same rules of arithmetic as finite numbers. In some cases, when the two infinite quantities are equal, they can cancel each other out resulting in a value of 0.
Yes, there are situations where infinity - infinity does not equal 0. This can happen when the two infinite quantities are not equal or when they are not well-defined.
No, infinity - infinity is a concept used in mathematics and does not have a direct real-world application. It is used to describe theoretical infinite quantities and cannot be measured or calculated in practical situations.