We recently conducted in-depth conversations about equity with 30 staff members of 15 foundations whose peers named them as leading “equity work” in the field. This is particularly true in philanthropy. We can say that zero over zero equals "undefined." And of course, last but not least, that we’re a lot of times faced with, is 1 divided by zero, which is still undefined.“Equity” is one of those terms that everyone seems to understand at some visceral level, but few people share the same definition. Just say that it equals "undefined." In summary with all of this, we can say that zero over 1 equals zero. Make sure that when you are faced with something of this nature, where you are dividing by zero make sure you don't put an actual number down, or a variable down. So, that means that this is going to be undefined. So, in this scenario the first part doesn't work. Because what happens is that if we can say that zero, 5, or basically any number, then that means that that "c" is not unique. But what I'm getting at is that it is the first part that is not being satisfied. We can actually plug in anything into there. Well, we can also put in a 5 if we wanted to because zero times 5 equals zero, so it still works for that second part. Because we’ve got zero which is our "b" times zero which is our "c," that does equal our "a" which is zero. Well, I think all of us can agree that we can obviously put in a zero there and the second part will be defined. Since it doesn't satisfy at least one part of that definition, then that means that it is considered "undefined." So this does not work and that means that it's going to be "undefined." Now, for our next example, sometimes we come across this idea where we actually have zero divided by zero. So it doesn’t satisfy this part of the equation. We don't get what "a" is because of course, zero times zero does not equal 1. We take our "b" which is zero and multiply it by our "c" which is zero. And a lot of people like to guess that it would be zero. Our next example is going to be 1 divided by zero.
We can say that zero divided by 1 equals zero and we can also say that this is "defined" as well. So it satisfies that this is actually the only number that you can put there to actually equal zero. And this first part, if you were to plug in, say, a 1, a 2, or any other number, then it wouldn't equal that so we can actually say that "c" is unique.
It satisfies this second part of the definition. I am going to say that this equals zero because 1 times zero equals zero. So let me clear this, and let's start with zero divided by 1. Likewise, if it only satisfies one part of the definition, it would mean that it is "undefined." Let's look at examples with zero in them and see what happens to them. And we can also say that this is "defined" because it satisfies the whole definition of division. So that means that 6 divided by 2 does equal 3. So our "b" is 2 times "c" which is 3 equals "a" which is our 6. If we multiply our "b" times "c" then we should get "a".
We can also figure out what the second part means. 3 is unique because we know that 3 is the only number that equals 6 divided by 2. So let's say that 6 divided by 2 equals 3. The definition of division states that if "a" divided by "b" equals "c" and "c" is unique, then "b" times "c" equals "a." So let’s do something - divide two numbers that we know. But first, what we need to do is familiarize ourselves with the definition of division. In this video we’re going to explore why dividing by zero is undefined.
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