7-4+3x0+1=?

Earlier this week I presented my Facebook friends with a math problem I found from a jokster I follow on Google+. While the original intent of the problem was to spark a funny debate, I found a deeper meaning behind it all.

Have you ever asked your math teacher in school "What am I going to be using this for?" or "Why on earth do I need to know all of this?" I did; all the time. However, they would always tell me to not that ask that question, or they just wouldn't acknowledge me. No one has ever given me a straight answer; but this single math problem tells you why.

Before I get to the explanation of the philosophical, let's try to solve the practical, shall we?

If you go by the old elementary rule of "Anything times zero equals zero" then you'll end up with "1" as the solution, as everything before the 0 can be disregarded since it becomes multiplied by 0. Then, just add the 1 and you're all set. About half of everyone in the Google+ debate provided "1" as the solution; and about the same on Facebook did as well.

But what about "Please-Excuse-My-Dear-Aunt-Sally"? If you went with the more advanced PEMDAS route (Parenthesis, Exponent, Multiply, Divide, Add, Subtract) then the answer would actually be "4". All calculators will actually confirm this answer.

7-4+3x0+1 (cancel out the 3x0)

7-4+1

3+1

=4

According to the almighty Wikipedia, PEMDAS (the Order of Operations, as it's officially named) is supposed to be unambiguous; meaning, it is absolute. But is the Order of Operations absolute, or is it the absolute? In other words, should we always use PEMDAS, no matter what? Or are there certain times when PEMDAS comes into play and then the order is absolute?

If the order itself is absolute, then the answer would actually be "2", not "4". How? Because if you follow PEMDAS to the letter (Ha! I made a funny!), then subtraction would be last, not first, and the answer would be 2.

7-4+3x0+1 (cancel out the 3x0)

7-4+1 (add first, subtract last)

7-5

=2

So in the long run, we have three possible answers: 1, 4, and 2. In other words, we have the practical approach (anything multiplied by zero is thus), the fluid approach (why does the calculator dictate a different approach to PEMDAS?), and the fundamental approach (the Order of Operations is absolute).

Anyone see the deeper meaning yet? This math problem isn't really a math problem; but a question about truth. When is truth absolute, and when is it relative? How can we determine such a thing? This is the reason why very few math teachers (no matter how well they exceed at the subject alone) can answer their students' long-time question: "Why do I need to know this?". Quite frankly, there is no absolute answer to the question. It all depends on when and how you use the methodology of mathematics.

For example: Most people would agree that 1+1=2; but that's because most people aren't computer programmers who would object to that statement if the problem was applied to the nature of computer science. 1+1=2 is a decimal system problem and solution; but according to thebinary system (that system of nothing but 1s and 0s in a computer's raw data stream), 1+1=10!

See, statements are often true because we define them to be so. And ifthat profound statement doesn't get you wondering about a plethora of things right now, then I don't what will.

Reviews

[mikeymikemike]

I realize this is old, but this thing is floating around fb again, so this will come up. You are trying to make an interesting point, and I hate to "pooh, pooh" that, but...Your basic thesis is incorrect. As was mentioned in the other comment. I wanted to put it less subtly for future readers. This is a completely unambiguous problem. There's only one correct way to do it. The rules were specifically written to let mathematicians get the same answer to the same problems, to avoid this issue. NOBODY EVER intended PEMDAS or whichever acronym you choose to mean "follow this in this exact order, i.e. addition has to come before subtraction." I'm not sure where you were looking for your "absolute" definition, but every convention says multiplying and dividing are EQUAL and done left to right, then adding and subtracting are EQUAL and also done left to right. The one and only correct answer is FOUR.

[gklivewire]

lol u did have me for a minute. I lite a smoke now im good

[Sneakygnome]

For 7 - 4 + 3 x 0 + 1 to equal 2 you are implicitly making the problem 7 - (4 + 3 x 0 + 1), which is equal to 7 + (-1)4 + (-1)(3 x 0) + (-1)(1) = 2.

Or you could say that 7 - 4 + 1 = 7 - 5 comes from incorrect manipulation of negative numbers, because, in truth, 7 - 4 + 1 = 7 - 3.

So the question of reality and truth is not one of definitions, but rather whether you are talking about the same problem and solving it correctly. :)

1 + 1 = 10, however, is a perfect example of how truth depends on what you define.

[Tegon Maus]

very interesting !! A truth is in the eye of the beholder kind of a thing ! I hear the same is true about beauty...

[Paul James]

Thanks for the review Tegon; and I would agree about beauty.