&nbsp;&nbsp;𝑇={𝑚∈ℤ|𝑚=1+(−1)𝑖,for some ineteger 𝑖}

To solve the given set equation:T={m∈ℤ∣m=1+(−1)i,&nbsp;for&nbsp;some&nbsp;integer&nbsp;i}We can break down the equation and determine the elements that satisfy the condition.The equation states that T is the set of integers m, such that m can be expressed as 1+(−1)i, where i is an integer.Let's examine the expression 1+(−1)i for different values of i:For i = 0: 1+(−1)·0=1+0=1For i = 1: 1+(−1)·1=1−1=0For i = 2: 1+(−1)·2=1−2=−1For i = 3: 1+(−1)·3=1−3=−2...Based on these calculations, we can see a pattern emerging. The expression 1+(−1)i alternates between 1 and 0 as i increases. In other words, for every even value of i, the expression evaluates to 1, and for every odd value of i, it evaluates to 0.Therefore, we can express the set T as:T={m∈ℤ∣m=1&nbsp;if&nbsp;i&nbsp;is&nbsp;even,m=0ifiisodd}In set notation, this can be written as:T={1,0}Thus, the solution to the set equation is T=1,0.

"𝑇={𝑚∈ℤ|𝑚=1+(−1)𝑖,for some ineteger 𝑖}" was answered by our experts

High School
Math Word Problem

markvillalon19300

Answered question

2022-09-18

𝑇={𝑚∈ℤ|𝑚=1+(−1)𝑖,for some ineteger 𝑖}

Answer & Explanation

madeleinejames20

Skilled2023-06-04Added 165 answers

To solve the given set equation:

T = {m \in ℤ ∣ m = 1 + (- 1) i, for some integer i}

We can break down the equation and determine the elements that satisfy the condition.
The equation states that T is the set of integers m, such that m can be expressed as

1 + (- 1) i

, where i is an integer.
Let's examine the expression

1 + (- 1) i

for different values of i:
For i = 0:

1 + (- 1) \cdot 0 = 1 + 0 = 1

For i = 1:

1 + (- 1) \cdot 1 = 1 - 1 = 0

For i = 2:

1 + (- 1) \cdot 2 = 1 - 2 = - 1

For i = 3:

1 + (- 1) \cdot 3 = 1 - 3 = - 2

...
Based on these calculations, we can see a pattern emerging. The expression

1 + (- 1) i

alternates between 1 and 0 as i increases. In other words, for every even value of i, the expression evaluates to 1, and for every odd value of i, it evaluates to 0.
Therefore, we can express the set T as:

T = {m \in ℤ ∣ m = 1 if i is even, m = 0 ifiisodd}

In set notation, this can be written as:

T = {1, 0}

Thus, the solution to the set equation is

T = 1, 0

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