Size of a Special Subset

Let \( A \) be a subset of \(T = \{1, 2, \ldots, 100 \} \) subject to the condition that if 2 distinct elements \( a\) and \(b\) are in \(A \), then \(a+b\) is not in \(A \). What is the maximum value of \( |A| \), which is the number of elements in \(A\)?

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