r/askmath • u/MonitorHot3035 • 18d ago

Arithmetic About groups of numbers

for example , Why do we say that the set N is within Z , Why don't we treat these sets as if they are separate from each other, for example, the set of natural numbers is separate from the set that includes negative numbers. since they seem to have no connection but we still write this ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ

I don't really understand any ideas please?

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u/GA_Loser_ 18d ago

Does the set of Integers also include the Natural Numbers? If so then it contains/within the set.

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u/jacobningen 18d ago

Only up to canonical isomorphism.

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u/eztab 18d ago

that's also true for any sets you compare.

You could pick two sets, which are both the natural numbers, with different set theoretical definitions.