I saw this Reddit post today saying "My son's third-grade teacher taught my son that 1 divided by 0 is 0. I wrote her an email to tell her that it is not 0. ...
That’s not what division is though. Division, at least when talking about splitting a pizza, has 2 options.
The first is splitting it into X equal parts. If you split a pizza into 0 equal parts, how large is each part?
The other option with pizza would be to say you are splitting into some unknown number of slices of a specific size. if you split a pizza in to slices that are 0 inches wide, how many slices do you get?
Neither method gives any logical result when using 0 with regards to pizza.
I’m not super great at math, and the concept of division by zero has been somewhat confusing for me. It’s also been a bane to my existence as a programmer. To me, in both scenarios, it makes sense to get back the original number, because 0 equal parts and zero inches wide leaves the original pizza untouched. But I also accept that there are much smarter folks out there who know better than I do, so undefined or NaN is what it is.
The easiest way to explain divide by zero is to think of division as repeated subtraction. For a simple example of 4 / 2 we know that we would have to subtract 2 from 4 twice to reduce it to 0.
When we divide by zero we’re functionally asking how many times can we remove zero from the numerator until it is reduced to zero. We typically state the answer as infinity or NaN because we know that we could do this operation indefinitely without the numerator reducing to 0.
To me, in both scenarios, it makes sense to get back the original number, because 0 equal parts and zero inches wide leaves the original pizza untouched
To illustrate why it’s not the original number, ask yourself this question — “How many times can you slice a pizza such that each slice is 0 inches wide?”
Yes, you’re leaving the pizza untouched with each slice, so you will never stop slicing. Or, you will say zero, because slices that are 0 inches wide are not slices at all. Or you’ll just say it can’t be done.
If I have one whole pizza, and I divide it zero times, then wouldn’t I still have one whole pizza? I.e., shouldn’t
1 / 0 = 1?That’s not what division is though. Division, at least when talking about splitting a pizza, has 2 options.
The first is splitting it into X equal parts. If you split a pizza into 0 equal parts, how large is each part?
The other option with pizza would be to say you are splitting into some unknown number of slices of a specific size. if you split a pizza in to slices that are 0 inches wide, how many slices do you get?
Neither method gives any logical result when using 0 with regards to pizza.
I’m not super great at math, and the concept of division by zero has been somewhat confusing for me. It’s also been a bane to my existence as a programmer. To me, in both scenarios, it makes sense to get back the original number, because 0 equal parts and zero inches wide leaves the original pizza untouched. But I also accept that there are much smarter folks out there who know better than I do, so
undefinedorNaNis what it is.Thanks though for explaining it!
The easiest way to explain divide by zero is to think of division as repeated subtraction. For a simple example of 4 / 2 we know that we would have to subtract 2 from 4 twice to reduce it to 0.
When we divide by zero we’re functionally asking how many times can we remove zero from the numerator until it is reduced to zero. We typically state the answer as infinity or NaN because we know that we could do this operation indefinitely without the numerator reducing to 0.
To illustrate why it’s not the original number, ask yourself this question — “How many times can you slice a pizza such that each slice is 0 inches wide?”
Yes, you’re leaving the pizza untouched with each slice, so you will never stop slicing. Or, you will say zero, because slices that are 0 inches wide are not slices at all. Or you’ll just say it can’t be done.
In this example, when you say “divide it zero times”, what you are really saying is “divide it by 2, zero times”.
So 20=1.