Let S stand for the set of all natural numbers that are perfect squares, so S...

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Let S stand for the set of all natural numbers that are perfect squares, so S = {1,4,9,16,25,36,49,64,...). Show that the set S and the set of all natural numbers have the same cardinality by describing an explicit one-to-one correspondence between the two sets. (b) Take the set of natural numbers and remove a first 7 numbers from it. Then, show that this new set has the same cardinality as the set of natural numbers. (c) You have infinitely many piles of peanuts. In the first pile, you have one peanut; in the second pile you have two; in the third pile you have three; and so on. How many peanuts do you have? Does the set of all these nuts have the same cardinality as the set of natural numbers? If so, provide a one-to-one correspondence. If not, explain why not. Let S stand for the set of all natural numbers that are perfect squares, so S = {1,4,9,16,25,36,49,64,...). Show that the set S and the set of all natural numbers have the same cardinality by describing an explicit one-to-one correspondence between the two sets. (b) Take the set of natural numbers and remove a first 7 numbers from it. Then, show that this new set has the same cardinality as the set of natural numbers. (c) You have infinitely many piles of peanuts. In the first pile, you have one peanut; in the second pile you have two; in the third pile you have three; and so on. How many peanuts do you have? Does the set of all these nuts have the same cardinality as the set of natural numbers? If so, provide a one-to-one correspondence. If not, explain why not. Let S stand for the set of all natural numbers that are perfect squares, so S = {1,4,9,16,25,36,49,64,...). Show that the set S and the set of all natural numbers have the same cardinality by describing an explicit one-to-one correspondence between the two sets. (b) Take the set of natural numbers and remove a first 7 numbers from it. Then, show that this new set has the same cardinality as the set of natural numbers. (c) You have infinitely many piles of peanuts. In the first pile, you have one peanut; in the second pile you have two; in the third pile you have three; and so on. How many peanuts do you have? Does the set of all these nuts have the same cardinality as the set of natural numbers? If so, provide a one-to-one correspondence. If not, explain why not.

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