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DerKrebs [107]
3 years ago
14

How do you reflect yourself in the topic (filters)​

Computers and Technology
1 answer:
Gnesinka [82]3 years ago
6 0
In what topic ?? Please explain more
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Produce an infinite collection of sets A1,A2,A3, . . . with the property that every Ai has an infinite number of elements, Ai ∩
atroni [7]

Answer:

Produce an infinite collection of sets A1,A2,A3, . . . with the property that every Ai has an infinite number of elements, Ai ∩ Aj = ∅ for all i = j, and [infinity] i=1 Ai = N.

Explanation:

Solution

For n ∈ N,

define  A_n = {2 ^n−1  ,(3)(2n−1 ),(5)(2^n−1 ),(7)(2^n−1 ), . . .}

I.e. A_n is all odd multiples of 2^n−1 . We must show that these sets satisfy the desired properties.

• (Infinite Number of Elements).

It is clear that the set A_n = {2 ^n−1 ,(3)(2^n−1 )(5)(2^n−1 ),(7)(2^n−1 ), . . .}  has infinitely many elements.

• (Disjoint).

Given A_n and A_m with n ≠ m, we can assume, without loss of generality, that n < m. Suppose  that there existed some x ∈ A_n ∩ A_m. Then by definition of these sets, there exists some odd numbers k  and l such that x = 2^n−1 . k = 2^m−1  . l.

However since n < m, we have that n ≤ m − 1, and therefore we  can write 2^m−1 = (2^n )(2 i ) with i ≥ 0. Hence we have 2^n−1 . k = 2^n. 2 ^i. l  

Dividing both sides by 2^n−1 yields  k = (2)(2^i ) .l, which contradicts the assumption that k is odd. Therefore A_n ∩ A_m = ∅.

• (Union is N).

We want to show that  [infinity] i=1 A_n = N.

(⊆). Since each A_n is a subset of N, the union of these sets is a subset of N as well.

(⊇).Given any x ∈ N, we can write x = 2^n−1 . k for some n ∈ N where k is odd. Then x ∈ A_n, as  desired.

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When you see a yield sign what do you do?
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Your supposed to yeild to whatever is around its like a stop sign in a way
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On the attendance worksheet, in cell l5, enter an if function to determine if the percentage in cell k5 is greater than or equal
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=if(c5≥h18,(c5),(k5))

we will use if function to check the validity of function

we will first write the condition and then we will write the value if condition goes true otherwise if condition does not go true we will write false and function will return value in  k5 cell which we have provided in the formula.

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What do file management utilities do?
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D. make it possible for your OS to save, maintain, and access files.
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What is the full form of ABC​
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American Broadcasting Company

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