# What is Negative: Definition and 1000 Discussions

In mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset, a decrease in some quantity may be thought of as a negative increase. If a quantity, such as the charge on an electron, may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common-sense idea of an opposite is reflected in arithmetic. For example, −(−3) = 3 because the opposite of an opposite is the original value.
Negative numbers are usually written with a minus sign in front. For example, −3 represents a negative quantity with a magnitude of three, and is pronounced "minus three" or "negative three". To help tell the difference between a subtraction operation and a negative number, occasionally the negative sign is placed slightly higher than the minus sign (as a superscript). Conversely, a number that is greater than zero is called positive; zero is usually (but not always) thought of as neither positive nor negative. The positivity of a number may be emphasized by placing a plus sign before it, e.g. +3. In general, the negativity or positivity of a number is referred to as its sign.
Every real number other than zero is either positive or negative. The non-negative whole numbers are referred to as natural numbers (i.e., 0, 1, 2, 3...), while the positive and negative whole numbers (together with zero) are referred to as integers. (Some definitions of the natural numbers exclude zero.)
In bookkeeping, amounts owed are often represented by red numbers, or a number in parentheses, as an alternative notation to represent negative numbers.
Negative numbers appeared for the first time in history in the Nine Chapters on the Mathematical Art, which in its present form dates from the period of the Chinese Han Dynasty (202 BC – AD 220), but may well contain much older material. Liu Hui (c. 3rd century) established rules for adding and subtracting negative numbers. By the 7th century, Indian mathematicians such as Brahmagupta were describing the use of negative numbers. Islamic mathematicians further developed the rules of subtracting and multiplying negative numbers and solved problems with negative coefficients. Prior to the concept of negative numbers, mathematicians such as Diophantus considered negative solutions to problems "false" and equations requiring negative solutions were described as absurd. Western mathematicians like Leibniz (1646–1716) held that negative numbers were invalid, but still used them in calculations.

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2. ### Inequalities With negative numbers and switching x -- therefore switching the sign

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3. ### B How Can I Calculate Negative Multiplication Without Following Traditional Rules?

Say I have 6 pencils. I want to times this by negative two. Now ignoring the rules that your teacher taught you work this out. 6 pencils negative 2 times. Negative one time would be 0 and another negative times would be -6 right? So 6 x - 2 = -6 according to simple logic. The calculator will say...
4. ### I Negative area above x-axis from integrating x^2?

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5. ### I Gravity does negative or positive work with cosmos redshift?

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7. ### Probability of Negative Value in Sz 1/2 Spin System w/ Lambda 1 & 2

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10. ### A Negative slope in Williamson-Hall model

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11. ### Coulomb's law — A negative charge balanced between 3 positive charges

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12. ### I Negative energy when a laser goes through lithium niobate crystal?

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13. ### I Separation of Plasma into positive nucleus and negative electrons

Im wondering if plasma is possible to be separated into a positive nucleus and negative electrons and contained within a magnetic bottle ? If possible, what is the most efficient method of achieving it ?
14. ### The Impact of Negative Leap Seconds: Risks and Challenges for IT Systems

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15. ### B Is there some electrical charge that is neither positive nor negative?

I do not mean neutral electrical charge, but a forth kind (if exists) I am in 9th grade, and someone asked the teacher if there is an electrical charge that is not positive, not negative and not neutral, maybe something in the middle of them. The teacher said that there is a charge like that...
16. ### Work done in elevator problem — is it positive or negative?

Hi! So, I've actually already solved this problem.. for the most part. I have split up the work into two sections, floor 0 to 10, and floor 10 to 15. From floor 0 to 10, I did ## F_{elevator} = w_{pass.} + w_{elev.} ## ## F = (70)(20 (num. of pass.))(9.8) + (800)(9.8) ## ## F_{elev.} = 21560N...
17. ### How is the slope of the shear force equal to the negative of the load?

At any point between A and C the point load is negative (downwards), in the shear force diagram: positive is upwards, so this slope is negative. The equation says the slope should be positive. Is this something to do with shear force sign convention?
18. ### I Questions about Negative Pressure and Vacuum Energy

Currently, dark energy is described as a being that exerts a negative pressure while having a positive energy density. {\rho _\Lambda } + 3{P_\Lambda } = {\rho _\Lambda } + 3( - {\rho _\Lambda }) = - 2{\rho _\Lambda } However, there seems to be a problem with the negative pressure assertion...
19. ### MOS Capacitor under very large positive or negative bias conditions

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20. ### B Exploring Negative Energy at the Big Bang: A Non-Mathematical Explanation

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21. ### Negative Power Supply Clarification

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22. ### How do you know if the focal length is positive or negative?

In this problem, it doesn't tell you where is the focal length. So how do you know if it is in front or behind the object?
23. ### Understanding Electric Field of Positive & Negative Plates

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Summary:: Figure b also shows that there is no negative sign in Faraday's Law. How do I know when to include the negative sign?
25. ### I Interpreting Thermal Power in Cylinder with Source & Sink

I have a cylinder that is separated with an insulator. In the internal cylinder there is a thermal source, while outside the insulator we have a thermal sink. The power of the internal cylinder is positive, while of the external one in total is negative. How I should interpet the results. Like...
26. ### I Force between Positive and Negative Electrical Charges

I have in the past been criricised for inappropriate postings that I could have resolved with research so this time I have done the research first. The best solution I have found is from wiki "that causes it to experience a force when placed in an electromagnetic field." What causes the force...
27. ### Can this comparator accept negative voltage as its negative supply?

I check the datasheet of LM 319 high speed comparator online. I was wondering if LM 319 can accept negative supply voltage(-10V) and its possible to produce a 10V to -10V square wave which oscillates along origin rather than just 10V to 0v as shown below.
28. ### MHB B14 adding negative numbers

Find a. Subtracting 4 is the same as adding $\boxed{(-4)}$ b. Subtracting -7 is the same as adding $\boxed{(7)}$ c. Subtracting a positive number is the same as adding a \boxed{negative} number, where that $\boxed{?}$ is opposite of the original number d. Subtracting a negative number is...
29. ### Projectile negative vertical displacement

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31. ### XLR Port Negative Pin: ZRL & Ground Explained

Is zero reference level synonymous with the return path of a current, i.e., the negative wire? If so, where a ZRL is being used by a circuit, is the ground pin and the negative pin in a XLR port the same thing?

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33. ### Engineering Finding out the input impedance in a negative feedback op-amp

In this case, there is negative feedback. ##V_{out}## is almost equal to ##V_{in}## in this case. But I really can't understand how to even proceed to find out the input impedance in this case, from the equation I know. Can someone help me out in figuring how should I proceed?
34. ### Negative eigenvalues in covariance matrix

Trying to run the factoran function in MATLAB on a large matrix of daily stock returns. The function requires the data to have a positive definite covariance matrix, but this data has many very small negative eigenvalues (< 10^-17), which I understand to be a floating point issue as 'real'...
35. ### I Is there a negative sign in front of the centrifugal potential energy?

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36. ### B Energy & Pendulums: Is Negative Energy Real?

Does "absorbing" negative energy from gravity cancel the upward momentum of the pendulum? Or what? Where can I see energy being negative? Does it repel stuff? It sounds impossible.
37. ### Help With Negative Phases in a Numerical Term

I think I've got the numerator part figured out, but I'm really stuck on what to do with those negative phases in the last term and how to get this to all come together in the end. I feel like I must have made a mistake somewhere, but can't find it. Thanks in advance for the help!
38. ### I Negative Distance Metric: Elapsed Time & Space-Time Interval

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39. ### I Negative curvature in low dimensions

It's probably the hyperbola, but I don't see how it's curvature is negative. It looks like 2 parabolas. thanx, paige turner
40. ### I Improper density matrix with negative eigenvalues

Hi, there. I am working with a model, in which the dimension of the Hilbert space is infinite. But Since only several states are directly coupled to the initial state and the coupling strength are weak, then I only consider a subspace spanned by these states. The calculation shows that the...
41. ### Engineering Over-consolidation pressure / negative skin friction of clay

However, I can't find any proof on this ? Can someone help to explain this ?
42. ### MHB Modulus problem with a negative sign

In a video, a person discussed how to solve modulus problems with a negative sign. This is the link of that video lecture. He showed two methods to solve the problem. The first method is commonly used. Later he showed another method where he used a number line and a graph. Unfortunately, I...
43. ### MATLAB FFT of conjugate doesn't coincide exactly at the negative frequency

I am trying to understand why the conjugate of a signal in the time domain doesn't produce an exact flip of the frequency domain spectrum. There is always a one-pixel shift in the result. The MATLAB code is shown below. I use a flip for the conjugate spectrum to show that it doesn't match the...
44. T

### Negative Ease in knitting (both in flat rows and in rounds)

I am a knitter and am interested using physics to explain the negative ease we see in knitting especially in rib [ (k1, p1) rib for example). I think some could be explained by the stretch-ability of the materials, e.g. wool, acrylic, but is there a movement of the yarn in between the "live"...
45. ### I Checking for negative feedback in a circuit

This is the circuit in question. During lecture, when checking whether this was negative feedback, my instructor said that if the v_out increases, then v- increases as well, which would lead to the next v_out decreasing because v_out = A(v+ - v-). I get how if v- increases the next v_out would...
46. ### Is Nonconservative work negative?

I am a bit confused. My teacher solved this problem and his answer for the thermal energy produced was -147,000J. My book says it is 147000J. My teacher used the equation K2+P2=K1+P1+Wnc and my book used K1+P1=K2+P2+Wnc. Which one is it?

No.
48. ### Momentum Conservation: How to Reconcile a Negative Value?

Maybe a silly question but on the above question using the conservation of momentum: momentum before firing (0) = momentum after firing (55*35)+(M*2.5) If I re-range the above it's M = -(55*35)/2.5 = -770kg. I can I reconcile that minus sign (basically get rid of it)? Thanks

50. ### B Apparent missing negative phase oscillation energy - where is it?

When an oscillator produces waves - let's say they are highly focused - that are damped by a second negative phase oscillator, where is the wave energy? The energy in each set of waves must still exist. Has it become hidden?