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It's also the only real number that does not have an inverse element for multiplication (there is no number b such that (a * 0) * b = a)
by jakobegger 7y ago
It's also the only real number that does not have an inverse element for multiplication (there is no number b such that (a * 0) * b = a)
- james_s_tayler 7y agoThe integers form a group under multiplication though and a key property of a group is that every element has an inverse. So how does the definition hold if there is nothing that could be considered an inverse for the number 0? Curious about this... I never thought about it before.
- ulrikrasmussen 7y agoYou are thinking of the multiplicative group of integers coprime to some integer n. That set by definition never includes 0.
- jacobolus 7y agoThe integers do not form a group under multiplication. As you noticed, the multiplicative inverse of any integer other than 1 or –1 is not an integer. You might be thinking of the rational numbers (excluding zero).
- james_s_tayler 7y agoWoops. You're right. Looks like I need to play Group or Not Group. https://youtu.be/qvx9TnK85bw https://youtu.be/qvx9TnK85bw But then even for addition what's the inverse of 0? -0?
- MrQuincle 7y agoIntegers form a monoid under multiplication. PS: A monoid in which each element has an inverse is a group.