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Find identity element
Given:
\( a * b = a + b, \quad a,b \in I^+ \)
Identity Definition:
An element \( e \) is identity if:
\( a * e = a = e * a \)
Check:
\( a * e = a + e = a \Rightarrow e = 0 \)
But:
\( 0 \notin I^+ \)
Conclusion:
❌ Identity element does NOT exist in \( I^+ \)