Vanguard Alas!: Division by zero finally defined
Vanguard Alas!: Division by zero finally defined
Alas!: Division by zero finally defined
April 1, 2020
April 1, 2020

In Mathematics, a number cannot be divided by zero. This has been an ironclad rule set in place as far back as 628 CE, when Indian mathematician Brahmagupta first defined the number’s properties. One may go as far as examine the behavior of a number as it nears being divided by zero, but it will always yield an undefined result.

History, however, has been rewritten by Dr. Father Frank of the Mathematics and Statistics Department. The renowned mathematician broke the rule against division by zero by discovering its true value: hatdog. On March 14, the International Mathematical Union (IMU) recognized Frank’s findings following his submission to the acclaimed journal, Annals of Mathematics—an acclaimed academic journal that also contains all the proofs and solutions to many unsolved and enigmatic problems in the field.

## As stated by history

Brahmagupta’s work included division by zero—in which he asserted that zero divided by itself would result in zero itself. Afterward, around 850 CE, fellow Indian mathematician Mahavira extended Brahmagupta’s division property of zero, stating that dividing any number by zero is the numerator itself.

One of the long-held results of division by zero is the concept of positive or negative infinity—a discovery made by yet another Indian mathematician Bhaskara in 1150. Going strong for centuries, the widespread idea would remain true even in the time of Swiss mathematician Leonhard Euler, who publicized the concept under his German book Complete Introduction to Algebra in 1770.

Despite these mathematical leaps, they have all made an unfortunate error: they overlooked the fact that multiplication and division are reversible. That is to say if a number divided by zero is the numerator itself, then that result multiplied by zero must be the original number—which is untrue, as any number multiplied by zero is zero, based on zero’s multiplication property. Similarly, if the result of division by zero is infinity, then infinity multiplied by zero would yield different values depending on the numerator, which should not be the case for multiplication.

## The right path

Despite the seemingly impossible notion of division by zero, Frank reveals that the first step in deciphering this problem is to observe the behavior of the quotient that results from dividing a constant by divisors that approach zero. By approximating the values of the divisors as they approach zero, the answer may lead to either positive or negative infinity—depending on the polarity of the numerator.

Unfortunately, examining the behavior of a number as it keeps dividing numbers close to zero alone did not yield a definite value for dividing any number by zero. “It was simply unacceptable,” Frank says in an exclusive interview with The LuhSallian. “When I was a high school student, I used to struggle with results that ended up with division by zero. Empathizing with students who struggle with the same problem, I vowed to determine a definite result for this cryptic mathematical expression.”

After spending seven agonizing years pursuing this endeavor, the mathematician adopted an unorthodox approach by defying the words of his former college Mathematics professor whose name he conveniently could no longer recall. “He once told our class that we have to transform something that we do not know into something that we know. So why not do it the other way? Let us transform something that we know into something that we do not know,” Frank explains with roaring enthusiasm.

The rebellious and counter-intuitive effort paid off, as Frank managed to utilize the findings he acquired from observing the behavior of the result from dividing a constant by divisors that approach zero. Using the results, the mathematician created “antisymptote” numbers. “Remember those values that a mathematical equation approaches but can never quite reach? ‘Antisymptote’ numbers are those defined values that the equation can now be equal to; in this way, I am minimizing the notion of ‘close, but no cigar’ in Mathematics,” he explains.

## Savoring the value

With the value from division by zero becoming the first “antisymptote” number, Frank christened it as the hatdog value, a suggestion given by one of his graduate students. He further elaborates that “in the same way that we reject the conventional ‘close but no cigar’ in Mathematics, the hatdog value throws civility in problem-solving situations straight out the window.”

The hatdog value is symbolized by the capital Greek letter psi impaled to a bent, horizontally-elongated ellipse. He explains that the hatdog holds one of three possible values depending on the numerator, with the “virgin” and “mighty” value requiring a positive and negative numerator, respectively. The “tender” value bears precedence as it requires the numerator to be zero. “[In this regard,] the hatdog value is [similar to] hotdogs that have different fillings. It is beyond positive and negative infinity, which were the previous standard results,” Frank further clarifies, reiterating the superiority of the hatdog value.

Upon his submission of his revolutionary research on the hatdog value to the journal Annals of Mathematics, Frank acquired the stamp of approval from the IMU, along with a statement from the organization’s President, Carlos Kenig. “While the discovery can be described as ‘Mathematical!’, it disrupted the millennium-long knowledge about the undefined value across all fields of Mathematics. Nonetheless, the captivating name, combined with its hotdog-like symbol, will [undoubtedly] change—and hopefully elevate—the discipline of Mathematics,” Kenig concludes.