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Alt_Nim
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The program Wolfram Alpha say "True" but my friends want the Proof.
Could you help me please?
Could you help me please?
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Alt_Nim said:my friend said there are not equal because
he think about Aleph numbers in the set theory
what do you think about it?
For the opening poster's sake, I want to point out that while there are many infinite cardinal and ordinal numbers, none of them are called "infinity". The occasional use of the noun "infinity" in that context is a historical artifact of the time before people realized those number systems had more than one infinite element -- and I don't recall ever hearing a mathematician use the word "infinity" in that way.DrRocket said:There is a theory of cardinal number and a theory of ordinal numbers as well.
DR13 said:Depends on what infinities we are talking about. For instance, let us define group A as the amount of real numbers divisible by 2. Obviously, the size of group A is infinity. Now let us define group B as the amount of real numbers divisible by 10. Again, the size of group B is clearly infinity. However, our own logic tells us that there are five numbers divisible by 2 for every one number divisible by 10. Therefore, these infinities are not equal. Another instance of this would be have group A be the amount of real numbers between 1 and 2 and have group B be the number of real numbers between 1 and 3. Just another situation with different infinities.
What do you mean by size? Normally in that setting it's used to refer to cardinality -- and the two infinite numbers you defined really are equal.DR13 said:Therefore, these infinities are not equal.
DR13 said:sorry, i meant integers
Hurkyl said:What do you mean by size? Normally in that setting it's used to refer to cardinality -- and the two infinite numbers you defined really are equal.
You don't mean "logically interpret" you mean "intuit".DR13 said:I am just referring to how we would logially interpret it. Obviosly the gap between 1 and 3 is twice the size of the gap between 1 and 2
Yes, infinity is equal to infinity. This is because infinity is not a specific number, but rather a concept that represents something without an upper limit.
No, infinity does not have a numerical value. It is a concept that represents something without an upper limit, and cannot be expressed as a specific number.
No, infinity cannot be measured or calculated in the traditional sense. It is a concept that represents something without an upper limit, and cannot be expressed as a specific number.
No, infinity cannot be divided or multiplied in the traditional sense. It is a concept that represents something without an upper limit, and cannot be expressed as a specific number. However, certain mathematical operations involving infinity can be defined and used in certain contexts.
No, infinity is not a real number. It is a concept that represents something without an upper limit, and cannot be expressed as a specific number. In mathematics, infinity is often treated as an "ideal" concept rather than a real number.