Not only does he not have any money but he also owes Michael, who is not depicted here. So he actually has a negative net worth. Steve has a net worth of Steve's uncle cares about Steve and feels bad that he doesn't even have a 0 net worth; he has a negative net worth! And so Steve's uncle wants to at least take away some of this pain. He at least wants to get Steve back to a neutral net worth, a 0 net worth. So he decides to take away Steve's negative net worth. He wants to take away that What happens if you take away that -3?
Facing backwards and walking backwards might have us looking at 0 while we advance forward. If we care about the way we're facing, we need a more complex math object a vector to keep track of our orientation as well as position "14, facing forward" vs. Perhaps we'd use a line integral, moving along a path and tracking the direction we face as we go. Learn Right, Not Rote. Home Articles Popular Calculus. Feedback Contact About Newsletter. After thinking of a better intuition, here was my reply: Great question!
Imagine going on a walk. You're facing forward, and take 8 steps forward. Now, let's say we want to keep facing forward and take 6 more steps. Happy math. Appendix When doing simple arithmetic, we only track the final location, not orientation.
NOTE: This would be nicer with a few more images, but I can't find my phone charger right now so just try to draw the relevant pictures for yourself as you go through it. There exist two types of electric charges in the universe. We call them positive and negative charge. Think of a positive number as representing an excess of the positive type of charge on an object.
A negative number likewise represents an excess of negative charge on an object. But what happens when you add the negative type of charge to a positively charged object? Some of the charges will "neutralize" each other. Now what does subtracting charge mean? It means removing that much charge. Now look at the first picture I have above -- the one labelled Neutral.
But if I remove 2 blue negative charges, then there will be an excess of 2 red positive charges. Remember that the excess charge isn't the only charges in the object -- it's just that the rest of the charge is "neutralized". Just like in the "Neutral" image, you can think of this as a positive and negative charge stuck together and then behaving as it weren't charged at all. That's what subtracting a negative number means physically.
It sounds like the number of my pencils decreased by two, and the change is negative because there's one negative borrowing. Try thinking of subtraction as a special form of addition.
Instead of addition and subtraction being separate operations, subtraction is really addition in disguise and given a special name. Specifically, subtraction is when you perform addition with a negative number.
These are the same thing, it's just written differently so that the first case is addition while the second way of writing it is subtraction. That's why I say that subtraction is really addition in disguise. What is - -6? So instead of -6 which is a number 6 units below 0, we'll have the opposite of that: 6 units above 0, which is positive 6. Once this is clear, we can discuss your question:. I don't know if this will make any sense in the end. If you imagine the same number line as mentioned in the other answers, where positives going to the right and negatives are going to the left.
In this line, you'll start from 0 and your first instinct is to go right. Now we have to go left, by four steps. That Will place us right at the Doing the same for 2 - Starting from 0 and going right, We land at 2 again. Now we encounter a - change direction , which means we have to change direction, going left and, right next to it, we find another - change direction , which makes us to go right again.
Ones are often hidden So, with parentheses added for clarity, we have:. Foobaz John wrote an answer I quite liked, however I'd like to give one that states less facts and maybe is friendlier for non-Mathematicians:. This is defined as an element that, when we give our group operation an element together with its inverse, the output is the neutral additive element.
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