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.
Homework Statement
If the vector B⃗ has a magnitude of 45.0 m and makes an angle of 60.0 ∘ with the +x axis, the vector -B⃗
choices:
1. has a magnitude of 45.0 m
2. has the same direction as B⃗ , but a magnitude of − 45.0 m
3.makes an angle of − 60.0 ∘ with the +x axis
4. has the opposite...
1.Homework Statement
The wave function for a wave on a taunt string is:
y(x,t)=(0.350)(sin(10(π)(t)-3(pi)(x) +(π)/4)
where x and y are in meters and t is in seconds. If the linear mass density(μ) of the string is 75.0g/m, (a) what is tha average rate at which energy is transmitted along...
Hello, I'm brand new to this site. I have a number of questions that I can't get answered by anybody.
I want to some how create negative pressure under the car to suck the bottom of a car down using Vacuum fans (like the 1970 Chaparral 2J Can-Am racing car ("sucker car").
I has some basic...
I'm a little confused over what constitutes negative and positive energy. I've heard it said that we have a zero energy universe because the mass of the galaxies, etc. counts as positive energy which is exactly balanced out by gravity, or the gravitational potential, which counts as negative...
Hello All,
We are trying to convert a vacuum leak test for medical devices (catheters) from a syringe based test to a pump based test.
The current guidelines call for purging air from the ID of the catheter under test with water (~1mL). The distal end of the catheter (tube) is blocked and the...
The following is invalid, since the operation is not defined when ##a, b < 0##: ##\sqrt{-1}\sqrt{-1} = \sqrt{(-1)(-1)} = \sqrt{(-1)^2} = \sqrt{1} = 1##. This is not correct, because ##ii = -1##. This shows that ##\sqrt{a}\sqrt{b} = \sqrt{ab}## is invalid when ##a, b< 0##.
However, say we have...
Since lnx is defined for positive x only shouldn't the derivative of lnx be 1/x, where x is positive. My books does not specify that x must be positive, so is lnx differentiable for all x?
This isn't actually a homework problem, but it is an example in a my textbook that I have a question about...
imgur link: http://i.imgur.com/2OglMH4.png
Ok, I wanted to clarify some things. I understand that current flowing from a positive terminal to a negative terminal represents a...
How would we define positive and negative work in terms of energy? When the force and displacement are in opposite directions, we say the work done by the force is negative. When the force and displacement are in the same direction, we say the work done by the force is positive. However, how we...
I would like to know the maximum voltage that a metal sphere can hold from applying negative charge to it.
My thoughts are that the maximum voltage is the breakdown voltage of the surrounding medium (air in this case). I assume that at that voltage, electrons would arc from the sphere to the...
Homework Statement
What is the volume of a solid formed by the area trapped between y= -x^2 and y= -2x rotated 360° around x-axis?
Homework Equations
V = ∫A(x)dx
The Attempt at a Solution
y=y
-x^2 = -2x
x^2 -2x = 0
x(x-2) = 0
This means that the two functions cross at x = 0 and x = 2
From x...
Homework Statement
I was just wondering whether the following notes I took on work in physics are accurate? Or have I got my understanding wrong?
Note on friction
Following from the example of the dragging object above…
The object stops because it loses kinetic energy due to friction.
How...
Homework Statement
Determine the tension cable A and B and the x , y , z reaction of the ball and socket joint at C .
Homework EquationsThe Attempt at a Solution
I let the reaction of ball and socket joint at C = Fx , Fy and Fz
Sum of force in z direction :
TA +TB +FZ= 400
Sum of force in...
I am an undergrad working in biophysics research, and I was hoping you guys may have input on a simple but strange problem I'm facing. I don't know if this is appropriate for this forum, but it is not an especially specialized or complex problem and I am desperate.
I am currently conducting...
Homework Statement
Arg z≤ -π /4
Homework EquationsThe Attempt at a Solution
I'm confused whether the answer to that would be more than -45° or less. Should the approach to arguments be the same as in negative numbers?
I'm having problem understanding why negative angle of cosine is a positive value but negative of sine is a negative sine angle?why is this so?can someone please help me with this confusion?
Thanks in advance!COS(-angle)=COS(angle)
Sin(-angle)=-Sine(Angle)
Homework Statement
Hi all!
The problem is - 'find the condition that all roots of $$f(z)=az^3+bz^2+cz+d=0$$ have negative real part, where $$z$$ is a complex number'.
The answer - $$a,b,d$$ have the same sign.
Homework EquationsThe Attempt at a Solution
Honestly, I have no clue about how to...
Hi,
I am working on a video capture project in which i am videoing the projectile of a ball that is being thrown in the air and trying to fit it to a curve for the expected trajectory of a projectile with quadratic drag.I am running into the issue that in order for my expected trajectory to fit...
Homework Statement
How many non-negative integer solutions are there to the equation
x1 + x2 + x3 + x4 + x5 < 11,
(i)if there are no restrictions?
(ii)How many solutions are there if x1 > 3?
(iii)How many solutions are there if each xi < 3?
Homework Equations
N/A
The Attempt at a Solution...
Hi everyone,
I've encountered a curious problem I just can't figure out, and any input would be much appriciated!This is a personal project I'm working on, and as far as I know, there is no one else working on exactly the same. However, the computational study of critical phenomena is quite...
Homework Statement
I was given the Brayton reverse cycle and asked to prove that the total heat is negative (hence the heat pump cools the system).
I was to assume that all the steps are reversible.
Homework Equations
An ideal diatomic gas.
1st step: adiabatic compression.
2nd step...
An exercise in my text requires me to (in MATLAB) generate a numeric solution to a given second order differential equation in three different ways using a forwards, centered and backwards difference matrix. I got reasonable answers for \vec{u} that agreed with each other (approximately) for the...
I know this has been asked before: "Why is there a negative in the Lagrangian: L = T - V"
I have read the answers and am not happy with them so I tried to formulate my own justification and now ask if anyone could comment on it?
First, I am not happy with those who say "Because it works and...
These questions shows my lack of understanding of the expanding universe specifically the Friedmann equation. Here is a quote from Brian Greene (The Fabric of the Cosmos, page 273): “The early universe provided an arena in which gravity exerted its repulsive side with a vengeance, driving every...
Homework Statement
What is the acceleration of a body which is moving in opposite direction(assuming negative velocity) and is speeding up?
Homework Equations
acceleration=the rate of which an object changes its velocity
The Attempt at a Solution
In my opinion, an object moves with a negative...
So, I'm to understand that "0 - -a = a" and I can understand this, in the context of say, being at an arbitrary reference point called "0" and then on a 2 dimension Cartesian graph of + shape and the operator "-", which can mean to reverse (so turn around 180 degrees) and then the second minus...
Hello,
I have been reviewing my textbook lately, and I came across a rather paradoxical statements. all of the convergence tests in my book state that the terms of the series has to be positive. However, when I solved this power series ∑(-1)n-1(xn/n), I found that it converges for -1<x≤1, but...
Homework Statement
https://www.google.se/search?q=f%C3%A4ltlinje&rlz=1C1_____enSE665SE665&espv=2&biw=1366&bih=643&source=lnms&tbm=isch&sa=X&ved=0CAYQ_AUoAWoVChMI9dTNgquLyQIVhJIsCh1NxQZU#tbm=isch&q=physics+field+lines&imgrc=rKecBAfLOMsOoM%3A
Why are the field lines on the positive atom pointed...
Homework Statement
The aim is to find a solution for the scale factor in a Robertson Walker Metric with a scalar field and a Lagrange multiplier.
Homework Equations
I have this action
S=-\frac{1}{2}\int...
Homework Statement
In the following question, in the solution, why is it that when they calculate the gravitational potential energy at point 2 (impact with spring), it is negative? I know that if both the force and displacement act in the same direction, then the work done should be positive...
Homework Statement
The problem I have is that we are asked to show the complex relative permittivity of a good conductor is erc = 1 + i(sigma)/(omega*epsilon_0) where sigma is the conductivity and omega is the frequency of an electromagnetic wave in the medium. This is fine, I calculated it...
Homework Statement
An error matrix is in the form, has a characteristic equation:
## CE: s^2 + 120s + 7200 = 0 ##
A state variable feedback system is described by:
## A_F = \begin{bmatrix}0 & 1 \\-616.8 & -40 \end{bmatrix} ##
## B = \begin{bmatrix}0 \\ 1 \end{bmatrix} ##
## C =...
Disclaimer: not sure if this is actually the most appropriate forum, but it is a question inspired by my work on a homework question...I'm happy for a moderator to move this to a different forum. (But General Physics states:
NO HOMEWORK/COURSEWORK QUESTIONS HERE)
1. Homework Statement
Ok...
What is meant by a negative distance on a sinogram in PET imaging?
http://frcrphysics.com/wp-content/uploads/2014/05/PET-sinogram.jpg
In this image displacement can be +ve or -ve. What would a -ve distance be?
Thanks
Homework Statement
Homework Equations
See above
The Attempt at a Solution
In the solutions guide for problem 71, if a charge is negative (look at the -1.5 C charge), it will be negative in the equation for potential energy (last step where multiplication brings 1.5J. On the other hand...
In the torque moment diagram of 4 stroke engine, there is a negative loop during suction stroke. Many books state that it is due to the higher atmospheric pressure. But, I do not understand the concept. Please help me understand why there is a negative and positive loop during suction and...
Homework Statement
An amount of work equal to 1.5 J is required to compress the spring in a spring gun. ?
Homework Equations
Wtotal = change of KE[/B]
The Attempt at a Solution
W=ΔKE=(1/2)m(Vf² - Vi²)
It sounds like the Vf >0 and would be maximum after the spring is compressed hard and...
Homework Statement
Consider the feedback loop involving Clouds, Rainfall and forest area.
All the relationships represented in this figure show positive couplings between the components:
Forest area is positively coupled to rainfall, plant evapotranspiration is positively coupled to forest...
Homework Statement
Train goes 20 m/s
Brakes cause a = -1 m/s2
Displacement at t = 40s ?Homework Equations
v = 20 m/s
a = -1 m/s2
t = 40s
The Attempt at a Solution
image upload no limit
It seemed like this formula fit perfectly. It had all of the known variables and the one unknown neatly out...
Homework Statement
[/B]
Find the position vector of point P if P divides AB in the ratio 5:-2 given A (-1,6,4) and B (4,1,-1)
The Attempt at a Solution
The only trouble I have is to understand the question...
Does it mean something like
A------------------>B<----------------------P...
Why potential at a point can only be obtained by supposing/assuming a positive test charge there?
For example
There was a question
In figure two points A and B are located in a region of electric field.,The potential difference ##VB##-##VA## is
1-positive
2-Negative
3-zero
4-none of the...
I'd like to know your views. Is it too good to be true? Or is there any obvious blunder?http://arxiv.org/abs/1509.07854
NUT wormholes
Gérard Clément, Dmitri Gal'tsov, Mourad Guenouche
(Submitted on 25 Sep 2015)
We show that supercritically charged black holes with NUT provide a new setting for...
I am missing something basic here. In https://en.wikipedia.org/wiki/Negative_energy, it is stated that "a universe in which negative energy dominates will either expand indefinitely or..." But gravitational potential energy is negative, so if I make the substitution, I would get "a universe in...
Hi , this may been asked quite a bit times but I can't really find a solid answer for this.
Do we have to include negative signs during calculations for vectors or scalars?
I have been told by someone that for vector quantity calculations such as Force we do not include the negative sign or...
Is there something wrong with negative probabilities per se? I don't what to hear that they are "unphysical" because it is not clear what reality is. Can negative probabilities (or probabilities > 1) be somehow consistent with macroscopic realism => not causing any macroscopic weirdness (no...
Homework Statement
http://imgur.com/RlIdmFh
http://imgur.com/3dnLK3m
Homework Equations
|x| = -x?
The Attempt at a Solution
I'm trying to make sense of this definition in my book because they are trying to prove the triangle inequality(second link), yet it keeps saying that the absolute value...
Using the potential energy formula -GMm/R^2 I understand that the maximum potential energy is 0. But what is the significance of the potential energy as it approaches negative infinity? I am not sure how exactly to word this, but I cannot seem to grasp the what negative potential energy tells us...
Suppose that you have N = \left(\frac{\partial U}{\partial \mu}\right)_{S,V} < 0, supposedly the number of particles, even though the actual number of particles is greater than zero. This means that you can have, in a system subjected to a grand canonical ensemble, less than 0 particle for...
Background
The teacher doesn't teach we just do activities and have whole chapters worth of 20 mini assignments due every few days. Yes I did read the book.
1. Homework Statement
Determine the signs (positive or negative) of the position, velocity, and acceleration for the particle in...