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Replaced the incorrect use of notation and terminology with the appropriate terms and symbols.
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As we know, there is a difference between the infinity(infinite) size (or cardinality) of the integer numbers and between the infinitysize of the reals ($\aleph_0$ and $\aleph_1$$\mathfrak c=2^{\aleph_0}$).

Who discovered it first?

As we know, there is a difference between the infinity of the integer numbers and between the infinity of the reals ($\aleph_0$ and $\aleph_1$).

Who discovered it first?

As we know, there is a difference between the (infinite) size (or cardinality) of the integer numbers and the size of the reals ($\aleph_0$ and $\mathfrak c=2^{\aleph_0}$).

Who discovered it first?

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peterh
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Who discovered the difference between the infinities?

As we know, there is a difference between the infinity of the integer numbers and between the infinity of the reals ($\aleph_0$ and $\aleph_1$).

Who discovered it first?