Solving a•b=(a+b)^2 with no Identity for Real Numbers

Thread starter Zashmar
Start date Apr 18, 2013
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The discussion centers on proving that the equation a•b=(a+b)^2 lacks an identity element for real numbers. An identity element, denoted as I, must satisfy the condition a•I= I•a= a. The participants conclude that there is no real number I that fulfills the equation (a+ I)^2= a for all values of a, thereby establishing the absence of an identity for the operation defined by a•b.

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Apr 18, 2013

Zashmar

Show that a•b=(a+b)^2 has no identity for real numbers
Hi this is a new topic please help
Thanks

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Apr 18, 2013

HallsofIvy

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An "identity" for an operation would be a member of the group, I, such at a•I= I•a= a. So you just need to show there is no number, I, such that (a+ I)^2= a for every a.