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If MC Z is a subset closed under addition and subtraction, then =dZ for some d € Z satisfying d≥ 0. `a, b € Z, then aZ + bZ = dZ and aZ ^ bZ = lZ, for suitable d, l = Z oes (aZ) (bZ) = abZ? Why is az U bZ of less interest here?

If MC Z is a subset closed under addition and subtraction, then =dZ for some d € Z satisfying d≥ 0. `a, b € Z, then aZ + bZ = dZ and aZ ^ bZ = lZ, for suitable d, l = Z oes (aZ) (bZ) = abZ? Why is az U bZ of less interest here?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Podasip 6. (a) If M ≤ Z is a subset closed under addition and subtraction, then M = dz for some d € Z satisfying d > 0. (b) If a, b & Z, then aZ + bZ = dZ and aZn bZ =lZ, for suitable d, l = Z (c) Does (az) (bz) = abZ ? Why is aZ U bZ of less interest here?
Transcribed Image Text:Podasip 6. (a) If M ≤ Z is a subset closed under addition and subtraction, then M = dz for some d € Z satisfying d > 0. (b) If a, b & Z, then aZ + bZ = dZ and aZn bZ =lZ, for suitable d, l = Z (c) Does (az) (bz) = abZ ? Why is aZ U bZ of less interest here?
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