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3. Infinite, abelian (and additive), and so that for every element a, a+a=0. (Hint: Think of infinite ‘vectors' (a₁, a2, ..., ak, 0, 0, 0, …) with all but finitely many co- ordinates equal to 0, and k is not fixed. Choose carefully where the non-zero coordinates a; come from.)

3. Infinite, abelian (and additive), and so that for every element a, a+a=0. (Hint: Think of infinite ‘vectors' (a₁, a2, ..., ak, 0, 0, 0, …) with all but finitely many co- ordinates equal to 0, and k is not fixed. Choose carefully where the non-zero coordinates a; come from.)

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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I have to give an example of a group that satisfies the stated property.

For Nr. 3 I have to find an infinite, abelian (and additive) group and so that for every element a, a + a = 0. (There is also a hint).

I don't really understand what they mean by the property a + a = 0. Can someone please explain?

I know that infinite, abelian and additive groups are for example the reals under addition, the integers under addition, the complex number under addition and the rational number under addition. 

I appreaciate any help, thank you!

3. Infinite, abelian (and additive), and so that for every element a, a+a=0. (Hint: Think of infinite ‘vectors' (a₁, A2,..., ak, 0, 0, 0,…) with all but finitely many co- ordinates equal to 0, and k is not fixed. Choose carefully where the non-zero coordinates a; come from.)
Transcribed Image Text:3. Infinite, abelian (and additive), and so that for every element a, a+a=0. (Hint: Think of infinite ‘vectors' (a₁, A2,..., ak, 0, 0, 0,…) with all but finitely many co- ordinates equal to 0, and k is not fixed. Choose carefully where the non-zero coordinates a; come from.)
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