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6. Mathematics / A. Nature of Mathematics / 4. The Infinite / b. Mark of the infinite

[what is distinctive about infinite numbers?]

3 ideas
A system S is said to be infinite when it is similar to a proper part of itself [Dedekind]
A collection is infinite if you can remove some terms without diminishing its number [Russell]
Infinite numbers are distinguished by disobeying induction, and the part equalling the whole [Russell]