Although related to the more mathematical concepts of infinitesimal , the idea of something being negligible is particularly useful in practical disciplines like physics, chemistry, mechanical and electronic engineering, computer programming and in everyday decision-making. A quantity can be said to be negligible when it is safe to ignore (neglect) it in the present case, within the margins for error that have been agreed to be acceptable in this case. In mathematics, an infinitesimal, or infinitely small number, is a number that is greater in absolute value than zero yet smaller than any positive real number. ...

Examples in electronic engineering

In order for electronic circuit designers to be able to think quickly and clearly through complex problems and complex circuitry, they are mentally equipped with a number of ideal circuit concepts that they use. These include the perfect voltage source, the perfect current source, the perfect amplifier, a perfect earth and many others. In mathematics, the term ideal has multiple meanings. ... An ideal voltage source, V, driving a resistor, R, and creating a current I A voltage source is any device or system that produces or can produce an electrical potential difference. ... An ideal current source, I, driving a resistor, R, and creating a voltage V A current source is an electrical or electronic device that delivers or absorbs electric current. ... A 741 operational amplifier in a TO-5 metal can package An operational amplifier or op-amp is a very high-gain amplifier which has two inputs, one inverting (−) and one non-inverting (+). The output voltage is the difference between the + and − inputs, multiplied by the open-loop gain: The... Ground symbols The term ground (or earth) usually means a common return path in electrical circuits. ...

In none of these cases can the perfect circuit element actually exist in practice. To take one example, consider the perfect voltage source. If a perfect voltage source existed, it would have no internal impedance and would continue to maintain its rated voltage, say 5 V dc, across any load, no matter what current may become necessary to do this. As the load impedance reduced toward zero ohms (a perfect short circuit - which also cannot truly exist) then the current flow and power delivery would approach infinity. This is simultaneously impossible, impractical and undesirable. So,rather than abandon the idea of the 'voltage source' we simply remember that the concept has limitations and work with them. To continue this example, we need to derive a specification for this practical voltage source. Perhaps we can say that the current draw will never exceed 2 amps. Perhaps we can say that input voltages between 4.999 V and 5.001 V will produce errors that in themselves are negligible for the practical purposes of the remaining circuitry. If the output impedance of the voltage source can drop 0.002 V (5.001 - 4.999) at a current of 2 A, it must be no more than 0.001 Ω or one milli-ohm. The output impedance, source impedance, or internal impedance of an electronic device is the opposition exhibited by its output terminals to the flow of an alternating current (AC) of a particular frequency as a result of resistance, induction and capacitance. ... This article may be too technical for most readers to understand. ... In electrical engineering, Impedance is a measure of opposition to a sinusoidal electric current. ... The ohm (symbol: Ω) is the SI unit of electric resistance. ... For alternate meanings see Short circuit (disambiguation) A short circuit (sometimes known as simply a short) is a fault whereby electricity moves through a circuit in an unintended path, usually due to a connection forming where none was expected. ... Jump to: navigation, search In electricity, current refers to electric current, which is the flow of electrons. ... Transmission lines in Lund, Sweden Electric power, often known as power or electricity, involves the production and delivery of electrical energy in sufficient quantities to operate domestic appliances, office equipment, industrial machinery and provide sufficient energy for both domestic and commercial lighting, heating, cooking and industrial processes. ... In engineering and manufacturing, the term specification has the following meanings: Technical requirement An essential technical requirement for items, materials, or services, including the procedures to be used to determine whether the requirement has been met. ... Jump to: navigation, search The ampere (symbol: A) is the SI base unit of electrical current equal to one coulomb per second. ...

Now we have a practical case - our voltage source with its negligible 1 mΩ output impedance will produce voltages that only deviate from 5.0 V by negligible amounts, provided the current requirements remain within spec.

In another case these discrepancies may be far too much as any voltage less than 4.999999 volts, or more than 5.000001 V, would be unacceptable. This is no problem, we just tighten our specification - there is always a practical limit.

In yet another case we may have a good 12.0 V supply available and a requirement that any voltage between 4V and 6V will be acceptable and that no more than 2 mA will ever be drawn. In this case a couple of 2 kΩ resistors in a simple voltage divider may suffice as a voltage source. This is hardly ideal, but it meets the requirements. An ideal resistor is a component with an electrical resistance that remains constant regardless of the applied voltage or current flowing through the device. ... In electronics, a voltage divider or resistor divider is a design technique used to create a voltage (Vout) which is proportional to another voltage (Vin). ...

The important point in the latter example is that, once drawn or soldered in place, the electronic engineer will continue to look upon the voltage divider, to a first approximation, as an ideal voltage source because as far as this requirement is concerned, that is what it is. Its practical discrepancies are negligible compared to the specification at this point. It is an important part of the engineer's skill, however, always to remember the assumptions and simplifications inherent in this thinking and to be able quickly to identify when cost savings can be made by reducing a specification requirement as well as when new requirements invalidate previously acceptable assumptions.

Similar examples could be created for any of the 'ideal' circuit elements listed above, and many more, from RF frequency mixers to the simplest switch. Jump to: navigation, search In telecommunication, a mixer is a nonlinear circuit or device that accepts as its input two different frequencies and presents at its output (a) a signal equal in frequency to the sum of the frequencies of the input signals, (b) a signal equal in frequency to... Jump to: navigation, search Electrical switches. ...

Examples in probability

It means,, That's straight~

Examples in software engineering

One might expect that a deterministic thing like a piece of software does not suffer from the vagaries of the negligible but this is not the case in at least two areas. In mathematics, a deterministic system is a system in which no randomness is involved in the development of future states of the system. ...

Digital representation of real-world variables

A computer system's internal representation of floating point numbers may normally approximate so closely to real numbers as to produce only negligible errors under most circumstances, but if, one day two very similar such values are subtracted, the result may be very far from what should be expected. A floating-point number is a digital representation for a number in a certain subset of the rational numbers, and is often used to approximate an arbitrary real number on a computer. ... Please refer to Real vs. ...

There are many other ways that assumptions about the "negligible" errors involved in these digital representations may cause problems at run time or later including analogue to digital conversion where resolution and bit-rates are necessarily limited, financial calculations where floating points or other imprecise number systems do not 'take care of the pennies' etc. All of these have something in common with the electronic engineering issues discussed above, although they are different in nature. In computer science, runtime describes the operation of a computer program, the duration of its execution, from beginning to termination (compare compile time). ... This article or section should include material from AD converters In electronics, an analog-to-digital converter (abbreviated ADC, A/D, or A to D) is a device that converts continuous signals to discrete digital numbers. ... Finance addresses the ways in which individuals, business entities and other organizations allocate and use monetary resources over time. ...

Interaction with the outside world

Digital systems that interact with the outside world, whether though a keyboard and mouse, a network or even via a disk drive gain a element of risk that also must be considered. There is a chance that the user may click another button before this calculation is complete, the network may be flooded with requests for this service quicker than the software can provide it or the disk may be full when we try to write to it, or the file we need to read may have been deleted or moved. A computer keyboard is a peripheral modelled after the typewriter keyboard. ... Operating a mechanical 1: Pulling the mouse turns the ball. ... Jump to: navigation, search A wide variety of systems of interconnected components are called networks. ... Disk Drive is the afternoon show on CBC Radio Two. ...

Modern computer programming languages provide the mechanism of throwing and catching exceptions so that the developer can handle these and many other possibilities without making the structure and logic of their code impenetrably complex to readers and future developers. Some languages, for example java, are designed to remind the developer about the exceptions that may be thrown — and so that should be caught, handled or declared of negligible interest — at each point. Others, like C#, provide the mechanism but do not enforce the practice in this way. In software engineering, a design pattern is a general solution to a common problem in software design. ... Jump to: navigation, search Exception handling is a programming language construct or computer hardware mechanism designed to handle runtime errors or other problems (exceptions) which occur during the execution of a computer program. ... Java is a reflective, object-oriented programming language developed initially by James Gosling and colleagues at Sun Microsystems. ... The title given to this article is incorrect due to technical limitations. ...

These examples are related to probabilities introduced by the IO systems of the computer. Input/output, or I/O, is the collection of interfaces that different functional units (sub-systems) of an information processing system use to communicate with each other, or to the signals (information) sent through those interfaces. ...

See also

• Resistor
• Capacitor
• Inductor

• Voltage source
• Current source
• Open circuit
• Short circuit

• Diode
• Transistor

• Operational amplifier
• Frequency mixer