Re: A business loss
No. You haven't in any sense 'lost' anything, you just charged less than you'd like to have charged. It's a little like when I tell people that I lost the lottery; I bought a ticket which wasn't the winner, so I say jokingly that I lost $42 million. Obviously I didn't; I DID lose a dollar, though.
Think of deductions as being against income, something you subtract from income.
In my lottery example, I can't claim that as a deduction, by the way, unless I'm using it to offset winnings from gambling.
You COULD show it as a deduction if you were simultaneously declaring your full price as the income. But you shouldn't really do that, either.
One might do that in an accrual accounting system, but the net result of course, the net income, is the same. But even in an accrual accounting business, people don't usually book the retail price as income and then call discounts deductions.