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Maatomaat
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How many kinds of infinity does math have?
in my point of view "THERE ARE INFINITY KINDS OF INFINITY"
What's your point?
in my point of view "THERE ARE INFINITY KINDS OF INFINITY"
What's your point?
Simon Bridge said:Welcome to PF.
Define "infinity" and explain, in terms of this definition, how there is more than one "kind", with an example. Then, perhaps, there can be meaningful POVs.
Maybe you are thinking of Cantor sets and the ideas around them:
http://www.scientificamerican.com/article.cfm?id=strange-but-true-infinity-comes-in-different-sizes
Maatomaat said:So they are different.
gb7nash said:The cardinality (size) of N and R are different, mainly due to the fact that N is countable and R is uncountable. Another reason is that there is also no 1-1 correspondence between N and R
Simon Bridge said:You still have to define your terms.
If you mean to demonstrate that there are different sizes of infinity, then please say so.
You seem to be having trouble communicating the ideas you want to discuss.
Have a look at how Cantor handled the same problem.
Do you mean the interval (0, 1)? If that's what you mean, the interval (0, 1) is NOT infinity, but the cardinality of this interval is infinity.Maatomaat said:Are you sure ? only "one" infinity?
We know "ℝ" is infinity.also "(1,0)" is infinity.
I can't see some of the symbols you wrote - they show up as squares in my browser. If you are saying that the interval (0, 1) can be placed on the real line, then what you are saying is incorrect. The cardinality of the interval (0, 1) is the same as the cardinality of the entire real number line.Maatomaat said:We can also say that we are able to place (1,0) on ℝ.so ℝ is more powerful than (1,0) so they are different.
No, I aren't.Maatomaat said:I mean ℝ-(1,0) is also infinity.
Please think about what I said. Are'nt you agree?
I cannot do any of these things because you have yet to define your terms.Are you able to prove that there is only one infinity or can you reject the flowing statement:
"N , R are infinity but R is not equivalent to N"
The concept of infinity refers to something that has no limits or boundaries. It is often used in mathematics and philosophy to describe something that is uncountable or never-ending.
There are two main kinds of infinity: potential infinity and actual infinity. Potential infinity refers to a process that can continue indefinitely, such as counting numbers. Actual infinity refers to a set or group that is already infinite, such as all the real numbers.
In mathematics, infinity is often used as a concept to describe uncountable sets, such as the set of all real numbers. It is also used in calculus to describe limits and infinite series.
No, infinity cannot be measured or compared in the traditional sense. It is a concept that exists beyond the realm of finite quantities and cannot be expressed in numerical terms.
The relationship between infinity and the universe is a subject of philosophical and scientific debate. Some theories suggest that the universe may be infinite, while others propose that it has a finite boundary. Additionally, the concept of infinity is often used to describe the vastness and complexity of the universe.