- #1
Loren Booda
- 3,125
- 4
In what regard might positive infinity be equivalent to negative infinity?
Define your terms. Then one may speak about what might be true.Loren Booda said:In what regard might positive infinity be equivalent to negative infinity?
Define your terms: only then can we start having discussions like this.Loren Booda said:If 2 times infinity is infinity, and 3 times infinity is infinity, thus a constant time infinity is infinity (proved by Cantor as aleph-0?), then it seems to follow that -1 times infinity [negative infinity] is infinity, or -2 times infinity [2 times negative infinity] is infinity, etc.
Again, define what you're talking about. Only then can such a question be meaningful. For example:Loren Booda said:Does the limit of C/x as x approaches zero from a positive direction equal the limit of C/x as x approaches zero from a negative direction?
Loren Booda said:Hurkyl,
Your explanation is sensible enough for me. Does 2 [a positive number] times infinity [an infinite cardinal number] have meaning?
How does one distinguish between projective and extended reals, in laymans terms?
Werg22 said:how can infinity equal minus infinity? Equality is property of finite numbers...
matt grime said:No it isn't.
Werg22 said:What do you mean? Of course if you were to talk about sets and other stuff, there's a tons of meanings for what equality is,
but Loren's question was algebraic I believe.
Really? So, Aleph_0+1=/=Aleph_0, or does it? Is there a meaning there?Edit: One could say infinity equals infinity all he wants, but it wouldn't mean anything mathematically, let alone infinity = - infinity.
noooo. there's only one. Your opbviosuly nonsensical assertion was that equality is something that pertains to numbers alone. I don't have to elucidate just why that is complete rubbish do I?
The expression "Oo = -oo" is a mathematical notation used to represent the concept of positive infinity being equivalent to negative infinity. In this notation, "Oo" represents positive infinity and "-oo" represents negative infinity.
In mathematics, infinity is not a specific number but rather a concept that describes something without any limit. Positive infinity and negative infinity are two different ways of representing this concept, where positive infinity represents numbers that are infinitely large and negative infinity represents numbers that are infinitely small.
Yes, there are several real-life examples that demonstrate the concept of "Oo = -oo". For instance, in the field of calculus, when calculating limits, we often encounter situations where the limit at positive infinity is equal to the limit at negative infinity. This is essentially the same as saying "Oo = -oo". Another example is in physics, where the concept of infinity is used in theories such as the Big Bang and black holes.
The concept of "Oo = -oo" is significant in mathematics because it helps us understand the properties of infinity and how it behaves in different mathematical operations. It also allows us to solve certain mathematical problems and equations that involve infinity.
No, "Oo = -oo" cannot be applied to all mathematical operations. It is mainly used in limits and certain algebraic equations. In other operations, such as addition and multiplication, infinity behaves differently. For example, infinity plus infinity is still infinity, but infinity times negative infinity is negative infinity.