|
|
real number
<mathematics> One of the infinitely divisible range of values
between positive and negative infinity, used to represent
continuous physical quantities such as distance, time and
temperature.
Between any two real numbers there are infinitely many more
real numbers. The integers ("counting numbers") are real
numbers with no fractional part and real numbers ("measuring
numbers") are complex numbers with no imaginary part. Real
numbers can be divided into rational numbers and irrational
numbers.
Real numbers are usually represented (approximately) by
computers as floating point numbers.
Strictly, real numbers are the equivalence classes of the
Cauchy sequences of rationals under the equivalence
relation "~", where a ~ b if and only if a-b is Cauchy with
limit 0.
The real numbers are the minimal topologically closed
field containing the rational field.
A sequence, r, of rationals (i.e. a function, r, from the
natural numbers to the rationals) is said to be Cauchy
precisely if, for any tolerance delta there is a size, N,
beyond which: for any n, m exceeding N,
| r[n] - r[m] | < delta
A Cauchy sequence, r, has limit x precisely if, for any
tolerance delta there is a size, N, beyond which: for any n
exceeding N,
| r[n] - x | < delta
(i.e. r would remain Cauchy if any of its elements, no matter
how late, were replaced by x).
It is possible to perform addition on the reals, because the
equivalence class of a sum of two sequences can be shown to be
the equivalence class of the sum of any two sequences
equivalent to the given originals: ie, a~b and c~d implies
a+c~b+d; likewise a.c~b.d so we can perform multiplication.
Indeed, there is a natural embedding of the rationals in the
reals (via, for any rational, the sequence which takes no
other value than that rational) which suffices, when extended
via continuity, to import most of the algebraic properties of
the rationals to the reals.
(1997-03-12)
Try this search on OneLook / Google
Nearby terms:
real hack « reality check « real mode « real number » real operating system » Real Programmer » Real Programmers Don't Use Pascal
This article was derived from the Free Online Dictionary of Computers and is available under ther terms of the GNU Free Documentation License.
Rave MP Sport 256MB MP3 Player w/FM TunerRave MP Sport 256MB MP3 Player w/FM Tuner ** Rave MP Sport MP3 Player with FM Tuner **You can take your music with you when you hit the pavement with this Rave MP Sport AMP256 digital audio player! Designed with adrenaline, thisRave MP Sport AMP256 delivers powerful, pulsating, skip-free music so you can crank up the burn.Order yours today!General Features:- Burgundy profile- 256MB Built-in Memory (Up to 8 Hours of Music) - Play Music from most online MP3 and WMA Services - Hi-speed USB 2.0 for Ultra-fast Music Transfers - Quick and Easy - Drag and Drop Music to and from PC - SD/MMC Memory Expansion Slot for Additional Storage - Plays 16+ Hours on 1 AAA Battery (Included) - FM Tuner with 20 Presets - Records Voice, Live Sound & FM Radio Operating Systems Supported:- Windows 98/ME/2000/XP - Mac OSX Regulatory Approvals:- FCCPlain Package Includes:- Rave MP Sport 256 MB MP3 Player- Sport Ear Buds- Armband- USB cable- One (1) AAA battery- Drivers CD Compatibility/Requirements/Disclosures:** Requirements *** Intel Pentium II 300 MHz or Above * 128 MB RAM Minimum * 150 MB Available Hard Drive Space * Available USB Port * CD-ROM Drive More ...
3-in-1 PS/2 KB/Mouse &Speaker Set - 2 for $19.993-in-1 PS/2 KB/Mouse &Speaker Set - 2 for $19.99 ** 3-in-1 PS/2 KB/Mouse & Speaker Set - 2 for $19.99 **Round out any great computer system with this 3-in-1 Mouse, Keyboard and Speaker Kit! Its white color will complement any environment!The PS/2 keyboard features 105-keys and multimediabuttons. The mouse features a scroll wheel to easilynavigate the web! The 2-piece speaker set has a volume control knob to adjust desired volume. These high quality components provide exceptional reliability at a fraction of the cost of other units sold individually!General Features:- White Keyboard, Mouse and 2-piece Speaker SetKeyboard Features:- PS/2 interface- Num Lock LED- Caps Lock LED- Scroll Lock LED- MultiMedia KeysMultiMedia Keys:- Back- Forward- Stop- Refresh- Search- Favorites- Web / Home- E-mail- Mute- Media- Volume Up- Volume Down- Previous- Stop- Play / Pause- Next- Calculator button- My Computer button- SleepMouse Features:- White mouse- PS/2 interface- Three buttons (scroll wheel acts as third button)- Scroll WheelSpeaker Features:- White- 2-Piece- Power LED- Power Button- Headphone in jack- Volume Control KnobRegulatory Marks:- FCC- CERetail Package Includes:- 3-in-1 Desk Manager Keyboard Mouse and Speaker Kit- MultiMedia Keyboard driver on floppy diskNotes:- Model: LK-7OID Compatibility/Requirements/Disclosures:** Requirements *** Microsoft Windows 95/98/NT/2000/ME/XP* Available PS/2 keyboard port* Available PS/2 mouse port* Available 3.5 mm standard audio jack* 1.44 MB Floppy Drive (to load driver) More ...
USB Rechargeable Battery Charger - 2 for $14.99USB Rechargeable Battery Charger - 2 for $14.99 ** USB Rechargeable Battery Charger - 2 for $14.99 **For use with AA and AAA NiMH and NiCD rechargeablebatteries (1800mA and 700mA),.Just connect the USB cable toa computer or laptop to start charging.General Features:- Charge two (2) or four (4) batteries at one time- Works with AA and/or AAA batteries- Works with NiMH or NiCD rechargeable batteries- Connects to your USB port on home PC or notebook- Charge LEDs- Full LEDs- DC 5v portCharging times:- AA batteries 1800mA approximately 285 min- AAA batteries 700mA approximately 90 minPackage Includes:- USB digital charger - Four (4) foot USB power tapRegulatory Marks:- CEPart Number: UTB-- > UPC: 8 002829 199882 Compatibility/Requirements/Disclosures:** Requirements* NiMH or NiCD rechargeable AA or AAA batteries* Available USB port More ...
Lowepro TX 500 Padded Video Camera Bag (Black)Lowepro TX 500 Padded Video Camera Bag (Black) ** Lowepro TX 500 Black Padded Video Camera Bag **Keep your video camera protected with this sleek, good looking and comfortable Lowepro TX 500 black padded video camera bag! Adjustable quick-release shoulder strap, 2 zippered outer side pockets, and its padded zippered main compartment makes this Lowepro TX 500 video camera bag not only useful but comfortable as well! Get yours today and travel in style! General Features: - Black - Contoured, padded, quick release shoulder strap - Two adjustable padded dividers - Large, padded, zippered front pocket with organizer - Padded DryFlo carrying handle - Zippered Side pockets - Tough, water-resistant outer material Exterior Dimensions: - 13.5W x 8D x 8.5H inches Inner Dimensions: - 9.5W x 3.25D x 6.25H inches Fits: - Digital Video Camera and batteries or small accessories - Compact Camcorder - Digital or 35mm SLR camera Notes: - Video Camera Bag Only - Model: TX 500 Compatibility/Requirements/Disclosures:** Requirements *** The need for a video camera bag More ...
Nvidia Geforce 2 MX 32MB AGP Video CardNvidia Geforce 2 MX 32MB AGP Video Card ** Nvidia Geforce 2 MX 32MB AGP Video Card **Compare at over $79.00!!!General Features:- Chipset: NVIDIA GeForce 2 MX200- NVIDIA 256-bit Hi Performance 2D and 3D accelerator engine equipped- AGP 2X /4X Support, AGP texturing, Fast Writes Support.- Equipped 32MB SDRAM 64 bit bus Interface running at 166MHz.- 175MHz core Clock, 350 million pixels/sec, 700 million texel/sec fill rate- 1.3GB/sec memory bandwidth- Second generation transform and lighting (T&L) engines- DirectX and S3 texture compression- 32-bit Z/stencil buffer- Complete support for DirectX 7.0 and DirectX 6.0, DirectX 5.0Notes:- Card only- Picture is for representational purposes only- IBM FRU 25P5848Compatibility/Requirements/Disclosures:** Requirements *** Available AGP slot* VGA monitor or better* Drivers (Not required for WinXP,2000 or Me) More ...
Intel PII 266MHz 66MHz 512KB Slot 1 CPUIntel PII 266MHz 66MHz 512KB Slot 1 CPU ** Intel Pentium II 266MHz 512KB 66MHz **- Standard Intel Pentium II Processor- 266 MHz- Slot 1, SECC Package- 66 MHz Bus Speed- 512KB L2 Cache- CPU Only Compatibility/Requirements/Disclosures:* Motherboard That Supports PII 266MHz CPUs* SECC Heatsink & Fan More ...
|
