In 1981, Joseph and Noriyo Aizawa (plaintiffs) purchased property and paid part of the purchase price with a $90,000 loan from the sellers. In return for the loan, the Aizawas gave the sellers a recourse mortgage on the property, which was secured by collateral. In 1987, the Aizawas defaulted on the loan repayments. At the time, the Aizawas’ basis in the collateral was $100,091.38. The sellers obtained a default judgment of $133,506.91 against the Aizawas, which included the loan’s principal, interest, attorney’s fees, and court costs. The collateral’s foreclosure sale price was only $72,700, which was the amount realized on the sale for the purpose of claiming a loss deduction under § 1001(a) of the federal tax code. The Aizawas applied § 1001(a) to claim a $70,898.29 loss on the foreclosure sale, a figure that the Aizawas derived by using a complex formula incorporating all of the relevant sums. The commissioner of internal revenue (commissioner) (defendant) subtracted the Aizawas’ mortgage principal from their basis in the collateral, and calculated that the Aizawas’ actual loss was only $10,091.38. The commissioner disallowed the balance of the Aizawas’ loss deduction. Aizawa filed a petition challenging the commissioner’s determination.