I have a theory that there are no negative numbers. is there any proof that negative numbers actually exist?

Question

the proofs that I find don't stand up, because first addition...

1 + -2= 1 - 2

yes, but the two being subtracted is actually a positive number, but the DIFFERENCE(a word used for subtraction) being shown the difference is that two is one more than, higher or away from one, therefore from one's point of view he has to look higher to see the two, therefore his gain on the two is made up of the figure negative one, but what is a negative gain, a gain is a gain, and a loss is a loss. Yesterday my friend, who's a police-man was told by his boss "Great job Parker! We gained so many losses today!" He's joking, and it's funny because it doesn't make sense logicaly, but you can understand what he's implying, still it is a form of deception, but mathematics is built on logic, and it's creed is that, there is no deceptiveness in simple numbers, only complexness, thanks, the other proof is about negative space or volume, but you only can measure it positively, that's my thought clarifi?

Answer 1

Numbers don't "exist". They are a concept we use to explain quantities. You have simply defined a different way to express a loss, a backwards movement, a deficit, et c.

We create numbers and operations (like addition, division, and square roots) to suit our informational needs (like putting groups together, dividing a group into several equal pieces, and measuring areas). You can create them in whatever way you choose, as long as the resulting system doesn't have inconsistencies with the physical world.

But don't try to fool your math teacher. Some of those folks have no sense of humor about these things.

Answer 2

Does subtraction exist? It usually is defined in terms of addition. For that matter, does addition exist? or positive numbers?

One way of looking at this is to say that one makes up rules (axioms) and then argues from there. If you say, "there exists an integer whose successor is zero" is an axiom, then in that system that integer exists by axiom and that integer is -1, a negative number. Once -1 exists, all negative numbers exist; for example, -9 = -1 x 9.

So one way of looking at it is that mathematics is a game you play with symbols. Something exists because you say it exists or because you can prove it exists from the axioms. Make up the axioms, and conclude the theorems. This is sometimes called the positivist view.

Another way is that there is something out there called -1 that exists regardless of us. When we start working with a number whose successor is zero, we discover -1, not invent it. Mathematicians who work from this point of view are sometimes called Platonists.

All this is because mathematics is independent of the real world and is self-sufficient without it. Math, however, was invented to explain the real world. In terms of the real world, whether negative numbers exist depend on what they measure. You can't have -4 cows in a pasture; if 4 cows were to wander into such a pasture, suddenly there would be nothing. But you can have -4 dollars in your check account, and you can go -4 miles west. (that's 4 miles east). Similarly, the diagonal of a square is sqrt(2) times as long as the side, although you can't get exact measurements of something in the real world. And a capacitance is an impedance in an electrical circuit that is best measured by using imaginary numbers, such as sqrt(-1).

So it depends on your point of view, and it depends on what your numbers measure, if they do measure anything.

Answer 3

i guess this thought is purely relativistic, since there really are no negative numbers but rather positive numbers that exist in the opposite direction, such as in graphs and the like, but you see there has to exist negative numbers because in science everything is merely looked at in a relativistic point of view, such as quantum mechanics which assigns a relativistic mass to an object that is essentially massless, so if we assign positive numbers mathematically we also assign negative number, there are things that can be explained mathematically which are really hard to explain physically because we have no way of measuring, similar to the example of wavelengths of matter. So in some respects you are right, but in others not so much. Depends if you look at it mathematically or physically.

Answer 4

Yes and No. Negative numbers are extremely useful when working with quantities that are described in more complex ways. For example, consider the change in velocity in one direction and the change in velocity in exactly the opposite direction. If this change is the same, then knowing only this quantity (or magnitude) of change tells us nothing about the direction, thus we are missing vital information. The change in velocity (acceleration/decceleration) is commonly known to be a vector quantity and not a scalar quantity. Vector quantities usually have magnitude and direction. So in this example, a negative acceleration is really decceleration. There are many other examples of vectors in physics. So, negative numbers 'exist' in physics but may not really 'exist' in simple math depending on your logic...

Answer 5

Negative numbers exist because we want to consider some position as zero. negative numbers can be converted into positive by shifting the zero as it happens in case of absolute temperature. Another thing: once we have numbers we define what is addition and then define subtractions as the reverse of addition. This creates negative numbers moment we reach zero. Numbers whether positive or negative do not exist They are our creation. Things do exist but numbers do not.

Answer 6

Yes, negative numbers do exhist. Even though you are really just subtracting. I can walk 3 steps forward and 7 steps back to arrive 4 steps backwards (in the negative direction) from where i started. Or if you have a negative number of apples in a basket it means you owe people apples.

Answer 7

No negative numbers exist? You should see my bank account.

Seriously, though, in the real world, negative numbers can exist to represent debt. Although with your arguement, those numbers actually represent a positive amount owed to someone else.

It's an interesting arguement, but not a unique one. See the Wikipedia article below.

Answer 8

Let c be the cardinality of the reals R. Then c = the cardinality of the non-negative reals R+ as well. Let aleph0 be the cardinality of the natural numbers, N. You want the cardinality of all functions from N to R+. It is c^aleph0. But c = 2^aleph0 and aleph0^2 = aleph0. So the answer is 2^aleph0, which is c.

Answer 9

Great analysis. I will suggest you take this to a lot of organizations that will use this in lots of PC campaings.

You may want to prove also that less is more, so less doctors will mean more healthcare for everyone. God bless you.

Answer 10

Take a peek ay my bank account and you will see that negative numbers, do in fact, exist.