See if you can follow this
Suppose we let:

A^{ }

=

B

Then Multiplying both sides by A, we get:

A^{2}

=

AB

Subtracting B^{2} from both sides, we get:

A^{2}  B^{2 }

=

AB  B^{2}

Factoring, we get:

(A  B)(A + B)

=

(A  B)B

Dividing both sides by (A  B), we get:

(A + B)

=

B

And since A = B, we can substitute B for A:

(B + B)

=

B

Dividing both sides by B, we get:

2B

=

B

And then:

2

=

1


Q. E. D.
Uhoh!
Can you find the flaw in the above "proof"? If so, you now know why we have one very important constraint built into our math system.
If you can't find the flaw, well . . . I could let you suffer . . . but then again, I hate seeing someone suffer so. So if you're one of the sufferers, send me an email or Comment on this Page and I'll explain the flaw to you.
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