State in each case, whether the given statement is true or false :
[1,2,3,1,2,3,1,2,3,……..] is an infinite set.

Answer

To determine whether the statement "[1, 2, 3, 1, 2, 3, 1, 2, 3, …]" is an infinite set, we can follow these steps:

### Step 1: Understand the definition of a set
A set is a collection of distinct elements. In this case, the elements are the numbers 1, 2, and 3.

### Step 2: Identify the elements in the given sequence
The sequence provided is [1, 2, 3, 1, 2, 3, 1, 2, 3, …]. Here, the numbers 1, 2, and 3 are repeated indefinitely.

### Step 3: Determine if the set is infinite
An infinite set is one that continues indefinitely without ending. In this case, the sequence continues with the same pattern of 1, 2, and 3 repeating over and over again.

### Step 4: Analyze the repetition of elements
Although the sequence appears to go on forever, we need to consider the distinct elements in the set. The distinct elements in this case are {1, 2, 3}.

### Step 5: Conclusion
Since the sequence keeps repeating the same three elements (1, 2, and 3), we can conclude that the set of distinct elements is finite, consisting of only three elements. Therefore, the statement that "[1, 2, 3, 1, 2, 3, 1, 2, 3, …]" is an infinite set is **false**.

### Final Answer
The statement is **false**.

---