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Hessam
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Some of my classmates were mentioning today that there are "different" values for infinity, like there is more than one infinity... can someone please help me? explain exactly what that means and what these values are please
Originally posted by Hessam
Some of my classmates were mentioning today that there are "different" values for infinity, like there is more than one infinity... can someone please help me? explain exactly what that means and what these values are please
Originally posted by BasketDaN
Positive and negative infinity both exist, but nothing else. You cannot have one more than infinity, or half infinity.
Originally posted by BasketDaN
It's really not that complicated at all. Infinity is a very commonly used term in calculus to describe a specific quality. The two differnet forms of this are positive and negative infinity. For instance, the Limit as n-->0+ of 1/(n) is inifnity. And the limit as n-->0 of ln(n) is negative infinity.
Did you read the previous responses in this thread? You can't just say "infinity"- that word applies to a number of different concepts. If you are talking about "cardinality" then, yes, the x-axis contains an infinite number of points- more precisely "c" points. In fact, any interval on the x-axis, say from x= 0 to x= 1 also has "c" points. But the x and y axes together have "c" points (I would not call that "infinity squared". I would call it "infinity plus infinity" if I were casual enough to write things like that. The number of points in the plane might be considered "infinity times infinity" but that is still "c" points. The x, y, and z axes together have cardinality "c" and the set of all points in 3 dimensional space has cardinality "c".Nizzy said:I have a question, because there is 'no end' to the possibilities of real number values, we can say that the x-axis (of a graph) has infinite points, right?
Now say we add the y-axis. As the y-axis is also a line, it has infinite point values as well right? So it would be infinity; and infinity times infinity is infinity squared. But because infinity squared is still considered an infinite value, would the value of both an x-axis' and a y-axis' infinity be greater than just that of an x-axis'?
If that's the case, would adding a z-axis provide a greater value of infinity than the previous two equations?
Ah, thank you for helping!
The concept of infinity is often associated with limitless or never-ending quantities. In mathematics, there are different types of infinity, such as countably infinite and uncountably infinite, which are used to describe the size of sets of numbers or other objects. In physics, infinity is often used in theories of the universe, such as the idea of infinite space or an infinite number of parallel universes.
In mathematics, infinity is defined as a concept of endlessness or limitlessness. It is often represented by the symbol ∞ and is used to describe numbers that have no upper or lower limit. Infinity is also used to describe the size of sets that have an infinite number of elements, such as the set of all real numbers.
No, infinity cannot be calculated or measured in the traditional sense. This is because infinity is a concept and not a specific number or quantity. It is often used as a theoretical concept in mathematics and physics, but it cannot be assigned a numerical value or measured physically.
Yes, there are different sizes of infinity in mathematics. This concept was first introduced by mathematician Georg Cantor in the late 19th century. He showed that there are different levels of infinity, with some infinities being larger than others. For example, the set of all real numbers is considered to be a larger infinity than the set of all natural numbers.
In science and technology, infinity is often used in theories and calculations to describe the vastness of the universe and to explain complex concepts. For example, in the field of computer science, infinity is used to represent a value that is too large to be stored in a computer's memory. In physics, infinity is used to describe infinite space or time, as well as in theories such as the multiverse hypothesis.