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66-648: [REDACTED] Look up rand in Wiktionary, the free dictionary. Rand may refer to: Money and business [ edit ] South African rand , the nation's unit of currency Krugerrand , South African gold coin Reasonable and non-discriminatory licensing , type of licensing used in the context of standardisation processes Rand formula , formula in Canadian labour law Randlord , term used to denote

132-515: A CSPRNG. Some classes of CSPRNGs include the following: It has been shown to be likely that the NSA has inserted an asymmetric backdoor into the NIST -certified pseudorandom number generator Dual_EC_DRBG . Most PRNG algorithms produce sequences that are uniformly distributed by any of several tests. It is an open question, and one central to the theory and practice of cryptography , whether there

198-724: A census-designated place in Kanawha County, West Virginia People [ edit ] Rand (given name) Rand (surname) Ayn Rand , Russian-American novelist and philosopher Rand Paul , American politician and physician. Rand (Robotech) , character from the fictional Third Robotech War Rand al'Thor , main protagonist in The Wheel of Time series by Robert Jordan Paul Rand , American art director and graphic designer Organizations [ edit ] RAND Corporation , an American think tank Ayn Rand Institute , an American think tank Rand Refinery ,

264-670: A function f : N 1 → R {\displaystyle f:\mathbb {N} _{1}\rightarrow \mathbb {R} } (where N 1 = { 1 , 2 , 3 , … } {\displaystyle \mathbb {N} _{1}=\left\{1,2,3,\dots \right\}} is the set of positive integers) a pseudo-random number generator for P {\displaystyle P} given F {\displaystyle {\mathfrak {F}}} taking values in A {\displaystyle A} if and only if : ( # S {\displaystyle \#S} denotes

330-658: A long period (see middle-square method ). Numbers selected from a non-uniform probability distribution can be generated using a uniform distribution PRNG and a function that relates the two distributions. First, one needs the cumulative distribution function F ( b ) {\displaystyle F(b)} of the target distribution f ( b ) {\displaystyle f(b)} : Note that 0 = F ( − ∞ ) ≤ F ( b ) ≤ F ( ∞ ) = 1 {\displaystyle 0=F(-\infty )\leq F(b)\leq F(\infty )=1} . Using

396-621: A massive sell-off in emerging economies." In 2014, South Africa experienced its worst year against the US dollar since 2009, and in March 2015, the rand traded at its worst since 2002. At the time, Trading Economics released data that the rand "averaged R4.97 to the dollar between 1972–2015, reaching an all time high of R12.45 in December 2001 and a record low of R0.67 in June of 1973." By the end of 2014,

462-744: A pile of quarried limestone (100 rand); the statue of Mandela at the Union Buildings in remembrance of when he was inaugurated there in 1994 (200 rand). On 3 May 2023, the South African Reserve Bank announced that a new series of banknotes would retain the image of Nelson Mandela on the obverse while showing the Big 5 in a family depiction on the reverse. This series contains the same denominations of 10, 20, 50, 100, and 200 rand. Pseudorandom number generator PRNGs are central in applications such as simulations (e.g. for

528-579: A random number c from a uniform distribution as the probability density to "pass by", we get so that is a number randomly selected from distribution f ( b ) {\displaystyle f(b)} . This is based on the inverse transform sampling . For example, the inverse of cumulative Gaussian distribution erf − 1 ⁡ ( x ) {\displaystyle \operatorname {erf} ^{-1}(x)} with an ideal uniform PRNG with range (0, 1) as input x {\displaystyle x} would produce

594-593: A random sequence. In other words, while a PRNG is only required to pass certain statistical tests, a CSPRNG must pass all statistical tests that are restricted to polynomial time in the size of the seed. Though a proof of this property is beyond the current state of the art of computational complexity theory , strong evidence may be provided by reducing to the CSPRNG from a problem that is assumed to be hard , such as integer factorization . In general, years of review may be required before an algorithm can be certified as

660-468: A simulation of the standard uniform distribution. An early computer-based PRNG, suggested by John von Neumann in 1946, is known as the middle-square method . The algorithm is as follows: take any number, square it, remove the middle digits of the resulting number as the "random number", then use that number as the seed for the next iteration. For example, squaring the number "1111" yields "1234321", which can be written as "01234321", an 8-digit number being

726-546: A special commemorative series of banknotes was released in commemoration of the 100th anniversary of Nelson Mandela's birth. This series includes notes of all denominations, 10, 20, 50, 100, and 200 rand. These notes will circulate alongside the existing notes. The notes depict the standard face of Nelson Mandela on the obverse. Still, instead of the Big Five animals on the reverse, they show a younger Mandela with different iconic scenes relating to his legacy. These scenes comprise

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792-639: Is a pseudo-random number generator for P {\displaystyle P} , where F ∗ : ( 0 , 1 ) → R {\displaystyle F^{*}:\left(0,1\right)\rightarrow \mathbb {R} } is the percentile of P {\displaystyle P} , i.e. F ∗ ( x ) := inf { t ∈ R : x ≤ F ( t ) } {\displaystyle F^{*}(x):=\inf \left\{t\in \mathbb {R} :x\leq F(t)\right\}} . Intuitively, an arbitrary distribution can be simulated from

858-492: Is an important factor in the cryptographic suitability of a PRNG, but not the only one. The German Federal Office for Information Security ( German : Bundesamt für Sicherheit in der Informationstechnik , BSI) has established four criteria for quality of deterministic random number generators. They are summarized here: For cryptographic applications, only generators meeting the K3 or K4 standards are acceptable. Given: We call

924-412: Is any way to distinguish the output of a high-quality PRNG from a truly random sequence. In this setting, the distinguisher knows that either the known PRNG algorithm was used (but not the state with which it was initialized) or a truly random algorithm was used, and has to distinguish between the two. The security of most cryptographic algorithms and protocols using PRNGs is based on the assumption that it

990-414: Is infeasible to distinguish use of a suitable PRNG from use of a truly random sequence. The simplest examples of this dependency are stream ciphers , which (most often) work by exclusive or -ing the plaintext of a message with the output of a PRNG, producing ciphertext . The design of cryptographically adequate PRNGs is extremely difficult because they must meet additional criteria. The size of its period

1056-589: Is required to have any confidence that a PRNG generates numbers that are sufficiently close to random to suit the intended use. John von Neumann cautioned about the misinterpretation of a PRNG as a truly random generator, joking that "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin." In practice, the output from many common PRNGs exhibit artifacts that cause them to fail statistical pattern-detection tests. These include: Defects exhibited by flawed PRNGs range from unnoticeable (and unknown) to very obvious. An example

1122-520: Is sometimes required, as illustrated by the following warning in the International Encyclopedia of Statistical Science (2010). The list of widely used generators that should be discarded is much longer [than the list of good generators]. Do not trust blindly the software vendors. Check the default RNG of your favorite software and be ready to replace it if needed. This last recommendation has been made over and over again over

1188-547: Is the Mersenne Twister (discussed below), which was published in 1998. Other higher-quality PRNGs, both in terms of computational and statistical performance, were developed before and after this date; these can be identified in the List of pseudorandom number generators . In the second half of the 20th century, the standard class of algorithms used for PRNGs comprised linear congruential generators . The quality of LCGs

1254-472: The Monte Carlo method ), electronic games (e.g. for procedural generation ), and cryptography . Cryptographic applications require the output not to be predictable from earlier outputs, and more elaborate algorithms , which do not inherit the linearity of simpler PRNGs, are needed. Good statistical properties are a central requirement for the output of a PRNG. In general, careful mathematical analysis

1320-577: The South African pound as legal tender, at the rate of 2 rand to 1 pound, or 10 shillings to the rand. The government introduced a mascot, Decimal Dan, "the rand-cent man" (known in Afrikaans as Daan Desimaal). This was accompanied by a radio jingle to inform the public about the new currency. Although pronounced in the Afrikaans style as / r ʌ n t / in the jingles when introduced,

1386-623: The Thai ฿10 coin , the pre-2018 Philippine ₱10 coin , the British £2 coin , and the Canadian $ 2 coin ), a specially serrated security groove along the rim and microlettering. On 3 May 2023, the South African Reserve Bank announced that a new series of coins would be released. These will have the same denominations as the previous series. The 10c will feature an image of the Cape Honey Bee,

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1452-506: The rand , ( sign : R ; code : ZAR ) is the official currency of South Africa . It is subdivided into 100 cents (sign: "c"), and a comma separates the rand and cents. The South African rand is legal tender in the Common Monetary Area member states of Namibia , Lesotho , and Eswatini , with these three countries also having national currencies: (the dollar , the loti and the lilangeni respectively) pegged with

1518-476: The 1 and 2-cent coins was discontinued in 2002, followed by 5-cent coins in 2012, primarily due to inflation having devalued them, but they remain legal tender. Shops normally round the total purchase price of goods to the nearest 10 cents. To curb counterfeiting, a new 5-rand coin was released in August 2004. Security features introduced on the coin include a bimetal design (similar to the €1 and €2 coins ,

1584-864: The 20c the Bitter Aloe, the 50c the Knysna Turaco , the R1 the Springbok , the R2 the King Protea , and the R5 the Southern Right Whale . The first series of rand banknotes was introduced in 1961 in denominations of 1, 2, 10, and 20 rand, with similar designs and colours to the preceding pound notes to ease the transition. They bore the image of what was believed at the time to be Jan van Riebeeck ,

1650-624: The EU would impact the South African economy and trade relations. In April 2017, a Reuters poll estimated that the rand would remain relatively stable for the rest of the year, as two polls found that analysts had already factored in a possible downgrade to "junk" status. At the time, Moody's rated South Africa two notches above junk status. When President Jacob Zuma narrowly won a motion of no confidence in South Africa in August 2017,

1716-1007: The Rand ( die Rand in Afrikaans), and associated urban area ( Greater Johannesburg ) East Rand , urban eastern part of the Witwatersrand West Rand , urban western part of the Witwatersrand Randburg , area in Gauteng province Midrand , area in Gauteng province Randfontein , a town in Gauteng province United States [ edit ] Randsburg, California Rand, Colorado , an unincorporated community in Jackson County, Colorado Rand, Texas , an unincorporated community in Kaufman County, Texas Rand, West Virginia ,

1782-526: The University of Johannesburg Science and technology [ edit ] rand, any of a number of pseudorandom number generator functions in various programming languages Rand index , technique for measuring the similarity between two data clusters R Andromedae (R And), a variable star Rand Airport , an airport near Johannesburg Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with

1848-456: The better-known previous Minister of Finance, Pravin Gordhan , would instead be appointed to the post. Zuma's surprise sacking of Nene damaged international confidence in the rand, and the exchange rate was volatile throughout much of January 2016 and reached an all-time low of R17.9169 to the US dollar on 9 January 2016 before rebounding to R16.57 later the same day. The January drop in value

1914-489: The contemporary pronunciation in South African English is / r æ n d / . One rand was worth US$ 1.40 (R0.72 per dollar) from the time of its inception in 1961 until late 1971, and the U.S. dollar became stronger than South African currency for the first time on 15 March 1982. Its value thereafter fluctuated as various exchange rate dispensations were implemented by the South African authorities. By

1980-558: The correct colour and were 1mm short. On 11 February 2012, President Jacob Zuma announced that the country would be issuing a new set of banknotes bearing Nelson Mandela 's image. They were entered into circulation on 6 November 2012. These contained the same denominations of 10, 20, 50, 100, and 200 rand. In 2013, the 2012 series was updated with the addition of the EURion constellation to all five denominations. They were entered into circulation on 6 November 2013. On 18 July 2018,

2046-677: The currency after that, most notably the 1994 general election , which had it weaken to over R3.60 to the dollar, the election of Tito Mboweni as the governor of the South African Reserve Bank , and the inauguration of President Thabo Mbeki in 1999, which had it quickly slide to over R6 to the dollar. The controversial land reform programme that was initiated in Zimbabwe , followed by the September 11, 2001 attacks , propelled it to its weakest historical level of R13.84 to

Rand - Misplaced Pages Continue

2112-434: The dollar in December 2001. This sudden depreciation in 2001 led to a formal investigation and a dramatic recovery. By the end of 2002, the currency was trading under R9 to the dollar again, and by the end of 2004, it was trading under R5.70. The currency softened somewhat in 2005, trading around R6.35 to the dollar at the end of the year. At the start of 2006, however, the currency resumed its rally and, as of 19 January 2006,

2178-431: The early 1980s, high inflation and mounting political pressure combined with sanctions placed against the country due to international opposition to the apartheid system had started to erode its value. The currency broke above parity with the dollar for the first time in March 1982. It continued to trade between R1 and R1.30 to the dollar until June 1984, when the currency's depreciation gained momentum. By February 1985, it

2244-746: The entrepreneurs who controlled the diamond and gold mining industries in South Africa in its pioneer phase Sperry Rand , an American technology company Places [ edit ] Rand, New South Wales , small town in Australia Rand, Lincolnshire , small village in Lincolnshire, England Brussels Periphery (Flemish territory around the city called Rand rond Brussel in Dutch, commonly shortened to de Rand ) South Africa [ edit ] Witwatersrand , escarpment running through Gauteng region, South Africa; commonly shortened to

2310-439: The first VOC administrator of Cape Town . It was later discovered that the original portrait was not, in fact, Van Riebeeck at all, but a portrait of Bartholomew Vermuyden had been mistaken for Van Riebeeck. In 1966, a second series with designs that moved away from the previous pound notes was released. Notes with 1, 5, and 10 rand denominations were produced with predominantly one colour per note. A smaller 1 rand note with

2376-430: The first quarter of 2008. This downward slide could be attributed to a range of factors: South Africa's worsening current account deficit, which widened to a 36‑year high of 7.3% of gross domestic product (GDP) in 2007; inflation at a five-year high of just under 9%; escalating global risk aversion as investors' concerns over the spreading impact of the sub-prime crisis grew; and a general flight to "safe havens", away from

2442-610: The number of elements in the finite set S {\displaystyle S} .) It can be shown that if f {\displaystyle f} is a pseudo-random number generator for the uniform distribution on ( 0 , 1 ) {\displaystyle \left(0,1\right)} and if F {\displaystyle F} is the CDF of some given probability distribution P {\displaystyle P} , then F ∗ ∘ f {\displaystyle F^{*}\circ f}

2508-512: The numbers were written to cards, they would take very much longer to write and read. On the ENIAC computer he was using, the "middle square" method generated numbers at a rate some hundred times faster than reading numbers in from punched cards . The middle-square method has since been supplanted by more elaborate generators. A recent innovation is to combine the middle square with a Weyl sequence . This method produces high-quality output through

2574-419: The past 40 years. Perhaps amazingly, it remains as relevant today as it was 40 years ago. As an illustration, consider the widely used programming language Java . Up until 2020, Java still relied on a linear congruential generator (LCG) for its PRNG, which is of low quality (see further below). Java support was upgraded with Java 17 . One well-known PRNG to avoid major problems and still run fairly quickly

2640-591: The perceived risks of emerging markets. The rand depreciation was exacerbated by the Eskom electricity crisis, which arose from the utility's inability to meet the country's rapidly growing energy demands. A stalled mining industry in late 2012 led to new lows in early 2013. In late January 2014, the rand slid to R11.25 to the dollar, with analysts attributing the shift to "word from the US Federal Reserve that it would trim back stimulus spending, which led to

2706-701: The previous five months, exchanging at a rate of R14.16 to the United States dollar. Following the United Kingdom voting to leave the European Union, the rand dropped in value over 8% against the US$ on 24 June 2016, the currency's largest single-day decline since the 2008 economic crash. This was partly due to a general global financial retreat from currencies seen as risky to the US dollar and partly due to concerns over how British withdrawal from

Rand - Misplaced Pages Continue

2772-507: The previous series, mainly because of the severe wear and tear experienced with low-denomination notes in circulation. In 1994, 100 and 200 rand notes were introduced. The 2005 series has the same principal design but with additional security features, such as colour-shifting ink on the 50 rand and higher and the EURion constellation . The obverses of all denominations were printed in English, while two other official languages were printed on

2838-473: The quality of the Mersenne Twister, which has a too-large state space and a very slow recovery from state spaces with a large number of zeros. A PRNG suitable for cryptographic applications is called a cryptographically-secure PRNG (CSPRNG). A requirement for a CSPRNG is that an adversary not knowing the seed has only negligible advantage in distinguishing the generator's output sequence from

2904-571: The rand at parity and still widely accepted as substitutes. The rand was also legal tender in Botswana until 1976 when the pula replaced the rand at par. The rand takes its name from the Witwatersrand ("white waters' ridge" in English, rand being the Afrikaans (and Dutch ) word for ' ridge '), the ridge upon which Johannesburg is built and where most of South Africa's gold deposits were found. In English and Afrikaans (and Dutch),

2970-522: The rand continued to slide, dropping 1.7% that day. In September 2017, Goldman Sachs said that the debt and corruption of Eskom Holdings was the biggest risk to South Africa's economy and the exchange rate of the rand. At the time, it had no permanent CEO, and Colin Coleman of Goldman Sachs in Africa said the company was "having discussions on solutions" on finding credible management. In October 2017,

3036-462: The rand firmed against the US dollar as it recovered from a six-month low. Reuters noted, "South Africa is highly susceptible to global investor sentiment as the country relies on foreign money to cover its large budget and current account deficits." On 13 November 2017, the rand fell by over 1% when the budget chief, Michael Sachs, stood down from his position in Zuma's administration. In October 2022,

3102-544: The rand had weakened to R15.05 per dollar, partly due to South Africa's consistent trade account deficit with the rest of the world. From 9–13 December 2015, over four days, the rand dropped over 10% due to what some suspected was President Jacob Zuma's surprise announcement that he would be replacing the Finance Minister Nhlanhla Nene with the little-known David van Rooyen . The rapid drop in value stemmed when Zuma backtracked and announced that

3168-492: The rand sank to its lowest point in two years, reaching R18.46 to the US dollar on 25 October 2022. Coins were introduced in 1961 in denominations of 1 ⁄ 2 , 1, 2 + 1 ⁄ 2 , 5, 10, 20, and 50 cents. In 1965, 2-cent coins replaced the 2 + 1 ⁄ 2 cent coins. The 1 ⁄ 2 cent coin was last struck for circulation in 1973. The 1 rand coin for circulation was introduced in 1967, followed by 2 rand coins in 1989 and 5 rand coins in 1994. Production of

3234-426: The reverse, thus using all 11 official languages of South Africa . In 2010, the South African Reserve Bank and commercial banks withdrew all 1994 series 200-rand banknotes due to relatively high-quality counterfeit notes in circulation. In 2011, the South African Reserve Bank issued defective 100 rand banknotes which lacked fluorescent printing visible under UV light . In June, the printing of this denomination

3300-529: The rolling hills of the Eastern Cape , featuring Mandela's humble birthplace of Mvezo (10 rand); the home of Mandela in Soweto , where he defined his political life alongside other struggle icons (20 rand); the site where Mandela was captured near Howick , following 17 months in hiding, where a monument to him has been erected (50 rand); the place of Mandela's 27-year imprisonment at Robben Island , showing

3366-431: The same design was introduced in 1973, and a 2 rand note was introduced in 1974. The 20 rand denomination from the first series was dropped. The practice of having an English and an Afrikaans version of each note was continued in this series. The 1978 series began with denominations of 2, 5, 10, and 20 rand, with a 50 rand introduced in 1984. This series had only one language variant for each denomination of note. Afrikaans

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3432-483: The singular and plural forms of the unit ("rand") are the same: one rand, ten rand, and two million rand. The rand was introduced in the Union of South Africa in 1961, three months before the country declared itself a republic . A Decimal Coinage Commission had been set up in 1956 to consider a move away from the denominations of pounds, shillings, and pence; it submitted its recommendations on 8 August 1958. It replaced

3498-427: The square of a 4-digit number. This gives "2343" as the "random" number. Repeating this procedure gives "4896" as the next result, and so on. Von Neumann used 10 digit numbers, but the process was the same. A problem with the "middle square" method is that all sequences eventually repeat themselves, some very quickly, such as "0000". Von Neumann was aware of this, but he found the approach sufficient for his purposes and

3564-520: The title Rand . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Rand&oldid=1135735720 " Categories : Disambiguation pages Place name disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages South African rand The South African rand , or simply

3630-408: The two-element field; such generators are related to linear-feedback shift registers . The 1997 invention of the Mersenne Twister , in particular, avoided many of the problems with earlier generators. The Mersenne Twister has a period of 2  − 1 iterations (≈ 4.3 × 10 ), is proven to be equidistributed in (up to) 623 dimensions (for 32-bit values), and at the time of its introduction

3696-500: The world's largest gold refinery Remington Rand , American computer firm and general manufacturer Ingersoll-Rand , diversified American industrial firm Rand McNally , American map publisher and printer Sperry Rand , American equipment and electronics company Rand Club , the oldest members club in Johannesburg Rand Afrikaans University , a defunct university that is now part of

3762-474: Was also partly caused by Japanese retail investors cutting their losses in the currency to look for higher-yield investments elsewhere and due to concerns over the impact of the economic slowdown in China , South Africa's largest export market. By mid-January, economists were speculating that the rand could expect to see further volatility for the rest of 2016. By 29 April, it reached its highest performance over

3828-435: Was known to be inadequate, but better methods were unavailable. Press et al. (2007) described the result thus: "If all scientific papers whose results are in doubt because of [LCGs and related] were to disappear from library shelves, there would be a gap on each shelf about as big as your fist." A major advance in the construction of pseudorandom generators was the introduction of techniques based on linear recurrences on

3894-634: Was moved from the South African Bank Note Company to Crane Currency's Swedish division ( Tumba Bruk ), which reportedly produced 80 million 100 rand notes. The South African Reserve Bank shredded 3.6 million 100-rand banknotes printed by Crane Currency because they had the same serial numbers as a batch printed by the South African Bank Note Company. In addition, the notes printed in Sweden were not

3960-451: Was running faster than other statistically reasonable generators. In 2003, George Marsaglia introduced the family of xorshift generators, again based on a linear recurrence. Such generators are extremely fast and, combined with a nonlinear operation, they pass strong statistical tests. In 2006, the WELL family of generators was developed. The WELL generators in some ways improves on

4026-468: Was short-lived; by the end of 1989, the rand was trading at more than R2.50 per dollar. As it became clear in the early 1990s that the country was destined for Black majority rule and one reform after the other was announced, uncertainty about the country's future hastened the depreciation until the level of R3 to the dollar was breached in November 1992. A host of local and international events influenced

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4092-469: Was the RANDU random number algorithm used for decades on mainframe computers . It was seriously flawed, but its inadequacy went undetected for a very long time. In many fields, research work prior to the 21st century that relied on random selection or on Monte Carlo simulations, or in other ways relied on PRNGs, were much less reliable than ideal as a result of using poor-quality PRNGs. Even today, caution

4158-457: Was the first language on the 2, 10, and 50 rand, while English was the first on the 5 and 20 rand. A coin replaced the 1 rand note. In the 1990s, the notes were redesigned with images of the Big Five wildlife species. 10, 20, and 50 rand notes were introduced in 1992 & 1993, retaining the colour scheme of the previous issue. Coins were introduced for the 2 and 5 rand, replacing the notes of

4224-486: Was trading at over R2 per dollar, and in July of that year, all foreign exchange trading was suspended for three days to try to stop the depreciation. By the time that State President P. W. Botha made his Rubicon speech on 15 August 1985, it had weakened to R2.40 per dollar. The currency recovered somewhat between 1986 and 1988, trading near the R2 level most of the time and breaking beneath it sporadically. The recovery

4290-399: Was trading under R6 to the dollar again. However, the rand weakened significantly during the second and third quarters of 2006 (i.e., April through September). In sterling terms, it fell from around 9.5% to just over 7%, losing some 25% of its international trade-weighted value in six months. In late 2007, the rand rallied modestly to just over 8%, only to experience a precipitous slide during

4356-405: Was worried that mathematical "fixes" would simply hide errors rather than remove them. Von Neumann judged hardware random number generators unsuitable, for, if they did not record the output generated, they could not later be tested for errors. If they did record their output, they would exhaust the limited computer memories then available, and so the computer's ability to read and write numbers. If

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