I am a math moron. Numbers just twist my brain into knots and have since they tried to reach me how to multiply in 3rd grade. (In spite of this, I managed to work as a bookkeeper for years. Successfully. Strange.)
In another thread, I brought this up and I would like to get more input, even though many people tried to answer it.
I accept because I am told to accept that multiplying any number by zero always results in zero. OK I’m not gonna argue that that’s not true.
However my brain resists it, and I use this example:
If I have one frisbee, a real frisbee that I can hold in my hand and tell you what color it is and throw it… And I multiply that frisbee by zero… Mathematically, I now have no frisbees at all. Even though I started with one. (Obviously, in the real world I still have that frisbee. So why does math take it away from me?)
How come?
(It makes sense rearranged: if I have no Frisbees to start with, multiplying zero frisbee by five frisbees can still give me zero frisbee because I didn’t start with a frisbee so it doesn’t matter how many times I’m multiply that zero it won’t become more unless you’re actually gonna say that multiplying no frisbees by 5 frisbees will give me 5 frisbees, In which case I will scream and go eat ice cream)
Multiplication is “How many of something do I have?”
If you have 1 of something (1x) you have one of them.
If you have ten of something (10x) you have ten of them.
If you have zero of something (0x) you have none of them.
Do you think this is going to help a self-described “math moron”?
I think of it like beowulff. You have zero groups of something. That is zero. Or you have a bunch of groups of zero. That is also zero. To me, it’s plenty intuitive.
You are unfamiliar with the word “moron”, I see. I am one. I was in remedial math for my entire school career, starting in 4th grade.
I think, based on later self education, that what you’re doing is sort of algebraic and I don’t do algebra. Although in my few encounters with scripting and computers, I find that I actually make better sense of algebra than I do real numbers because it’s the numbers that freak me out, not the mental gymnastics so much.
BTW, you frisbee scenario is confusing because you are not thinking about it correctly.
If you have a (1) frisbee, then you have 1* frisbee.
If you have NO frisbees, then you have 0 * frisbee.
So, if you start with a frisbee, you are done. If someone gives you another one, you now have 2 * frisbee. If someone steals the one you had, you now have 0 * frisbee. You can’t multiply the one you start with by some number, unless the you physically gain or lose frisbees.
Second quick and dirty reason
Multiplication can be thought as repeated addition
4x1 = 4; 4x2 = 4 + 4 = 8; 4x3 = 4 + 4 + 4 = 12.
Let me list all of the multiples of 4 starting with x1
4, 8, 12, 16, 20, … This is an arithmetic progression
Let me list all of the multiples of 4 starting with x -1 then x -2 then x -3, &c.
-4, -8, -12, -16, -20, … This is an arithmetic progression
So now I have all of the multiples of 4 except for x0. According to the arithmetic progression, what would that multiple be?
I did a second one for you while you were writing your reply. Check it out.
To put the first one into numbers so you see what is going on
5 x 0. Would you agree that 8 - 8 = 0? So we can substitute it in for 0
5 x (8 - 8) use the distributive rule to get rid of parentheses
5x8 - 5x8
40 - 40. Would you agree 40 - 40 = 0?
0
Third quick and dirty reason
A x B can be thought of as the number of squares in a grid A units wide and B units long
For example: if I have 6 x 9 then I ask how many squares are in a 6 by 9 grid? There are 54 of them so 6 x 9 = 54
Now how many squares are in the grid if the width is zero squares?
I believe this kind of questioning is very dangerous. People who wonder about this are likely to try to divide by zero and tear the structure of our universe into shreds. Sometimes I think people should need licenses to get a HP-11 or HP-15.
Is it the idea of zero that is the issue or the problem of multiplication?
I can write
Nothing plus nothing plus nothing plus nothing plus nothing …
as many times as I want and I won’t ever get Something.
I can write
Nothing plus nothing
and maybe this resembles
0 + 0
a little bit.
Instead of writing out “thing + thing + thing + thing + … + thing” for 100 times, we can save some time and express that more easily as “100 things”. If “thing” is a “dozen donuts”, how many donuts total? One dozen + one dozen + … + one dozen, one hundred times. But those clever math people came up with a symbol that saves time by expressing it like 100 x 12 donuts.
Similarly, nothing + nothing + … + nothing looks a lot like 0 + 0 + … + 0, and intuitively you know what the sum of all those 0’s will equal, even if I don’t tell you how many in a row I’m writing. But we can express this with that clever math symbol again like
[pick your favorite number] x 0 = ?
That little equation immediately above even works if your favorite number is 0.
If that’s unsatisfying, consider that advanced math moves away from the Real World pretty quickly and there is nothing in certain disciplines of math that have any Real World analogs or applications. Maybe 0 x 0 is your first brush with one of those.
What might be tripping you up is that you are starting with something, a frisbee. And then Evil Math takes it away when you do a perfectly legit multiplication.
What we are saying is that, when you are dealing with zero, there is no frisbee (nor a spoon, for that matter). It is a special case. There never was a frisbee.
Maybe it helps if if you think that times 2 is easy to understand in frisbee terms - you are doubling.
Times 1 means you still have the frisbee.
But times 0 is special and there isn’t an obvious real world equivalent action to perform on your frisbee.
(Similarly what does times -1 mean in frisbee terms? It’s a mathematical concept.)
I think your concern with the real world example is that you want to know what happened to the frisbee that you had. But the math is just a tool for counting the frisbees, not telling you how you got there.
So, maybe one of these examples would help:
You have a disc golf backpack that has 5 slots for frisbees. If each slot has 1 frisbee, then you have 5 frisbees. If each of the 5 slots has zero frisbees, then you have zero frisbees times 5 slots = zero frisbees. 5x0=0
To flip it around, think of it this way. You started the round of disc golf with one frisbee in each slot, 1x5, for a total of 5 frisbees. You’re terrible at disc golf. When you are done playing, there are no slots holding frisbees. We don’t know exactly how each one was lost, but we do know how to count up how many frisbees you have now. You put zero frisbees into each slot, so 0x5=0. Or, for each slot that can hold a frisbee, there are no occupied slots. 5x0=0.
You have to make up your own story about how they were lost. In math terms, how you got from 5 to zero is probably a story of subtraction in this case.
I saw the thread where this was originally discussed. It’s fascinating how different people think about concepts like this. I don’t know if any of these ways of looking at it will help, but it’s worth a shot.
Multiplying by zero is not a process that takes a number and transmutes it into another number. Multiplication takes two numbers and produces a third number as a result.
or
You can reverse the numbers in a multiplication problem and still get the same result. That doesn’t work in your example. If you have nothing and multiply it by 1 frisbee, what do you have? What does it even mean to multiply by a frisbee?
or
You have 1 frisbee. You think to yourself “I want to pack frisbees in boxes. 1 frisbee to a box, and I have 0 boxes.” The equation is “1 frisbee-per-box × 0 boxes = 0 frisbees in boxes” You still have the same 1 frisbee you started with. Maybe it’s on your lap, or on a table, or on the floor, but it’s not in a box. Nothing happened to it; it didn’t evaporate. The equation counts how many frisbees you have put in boxes, not how many you still own.
I think you are actually dividing by 0. You have 1 frisbee and you are trying to put it into 0 groups, which is division. That is mathematically undefined, so you are spot on with your intuition that it makes no sense.
If you have 1 frisbee 0 times, how many frisbees do you actually have? Whoever gave you that frisbee cheated, and didn’t actually give it to you. That’s what happened.