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, I, would satisfy the condition a•I= I•a= a for all a. Participants argue that to demonstrate this, one must show that no real number I exists such that (a+I)^2 equals a for every a. The conclusion drawn is that such an identity cannot be established within the realm of real numbers. Thus, the equation does not possess an identity element.

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.

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