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I am trying to explain how some infinities are larger than others in the easiest way possible. Here it is:

Imagine a supermarket that has every food item imaginable. (But it only has food.) In fact, it has infinite varieties of food. It also has infinite quantities of each item. It would be safe to say that this supermarket has infinite items of food.

Now imagine another supermarket that not only has every food item imaginable but also has every book ever written and infinite quantities of every book. It would be safe to say that this store has infinite items as well.

If we put the first supermarket into an equation, it would look like this: Let:
The first supermarket = X
The second supermarket = Y.
The number of food every food item imaginable and infinite quantities of each item = A
The number of every book ever written and infinite quantities of every book = B
Then:
A = ∞
B = ∞
X = A
Y = A+B
Y≥X
Therefore, X, which is infinite, is smaller than Y, which is also infinite.
Is this logic correct?

theknightD2
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    No. You haven't given any reason to imagine that one of those is more infinite than the other. That's the problem with infinity. Just because one infinite set is properly contained in another does not imply that one set has a higher order of infinity than the other. – lulu Sep 17 '21 at 14:16
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    No. You should have seen the example that for instance there are just as many even natural numbers as there are natural numbers... this despite the naturals consisting of the even numbers as well as the odd numbers. – JMoravitz Sep 17 '21 at 14:16
  • I recommend you study closely the concept of a bijection, then a little bit of cardinality, and return to this example. – While I Am Sep 17 '21 at 14:18
  • There are even "as many" algebraic numbers than natural numbers , a quite anti-intuitive matter. However, there are "more" real numbers in the interval $(0,1)$ than algebraic numbers. You have to study what "countable sets" are. – Peter Sep 17 '21 at 14:19
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    You may want to read about the Hilbert's hotel https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel – Vasili Sep 17 '21 at 14:19
  • Simple example: Number if even integers is infinite. Number of integers (all) is infinite. These infinities are equal. – herb steinberg Sep 17 '21 at 16:32

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