Mining Science Spring: Negative Number Multiplication or Division being equal to positive Number wrong Formulae Correction
明義科學之春﹕負數乘除法等于正數的錯誤的公式的改正
*XiaoPing Yi
(*[email protected], [email protected], [email protected])
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ABSTRACT
數字的加減乘除基本運算公式是初等數學內容。本作者忘了1970到1975年湖南省義務小學算術課本是否有負數乘除法公式﹐但義務初中代數肯定有。大約公元一世紀漢語“九章算術”書中沒有二負數乘除法公式。英語算術和數學書中有負數乘除法例題。乘法的本質是一些相同數的加法﹐例如﹐對于正數“A”﹐“A x 2 = A + A”﹐即二個A相加。除法的本質是計算平均值。方言“乘法 - xing fa 人法”表示許多加法的高速估算﹐例如﹐對于義立姓氏﹐一定地方的總豐收由乘法估算。在多姓氏集中之地﹐姓氏平均豐收由除法估算。負數的加減(gang)法舉例如下﹕“-1 + (-1) = -2”﹐“-2 - (-1) = - (2 - 1) = -1”。按照道理﹐或者推理和歸納邏輯法﹐因為A x 0 = 0﹐ 所以 A x (-1)小于 0。換言之﹐因為負數和正數或零的乘法公式是“-1 x 1 = -1, -1 x 0 = 0, -1 / 0 = 負無限, 0.1 x 0.1 = 0.01, 0 x 0 = 0, 0 / 0 = 不定數(無答案)”﹐又因為負數少于正數﹐所以“-1 x -1 < 0, -1 / -1 < 0”﹐這是負數﹐或者無答案。換言之﹐對于正數A和B﹐“-A x -B < 0, -A / (-B) < 0”。
Number addition, subtraction, multiplication and division basic operation formulae are part of duty elementary mathematics. The author forgot whether or not the year 1970 to 1975 Hunan province duty elementary arithmetic textbook has negative number multiplication and division formulae, but the duty lower middle school algebra surely has. In English arithmetic and mathematics books, there are example problem on negative numbers multiplication and division. First century A.D. Chinese book "九章算術 nine chapters of arithmetic" did not have formulae for two negative number multiplication and division. The essence of multiplication method is the addition of the same numbers, e.g., for positive number "A", "A x 2 = A + A", i.e., addition of two "A". The essence of division is to calculate average value. Dialect "乘法 - xing fa 人法 person method" indicates high speed estimation of many additions, for example, for independent surname man, the total harvest at a certain place is estimated by multiplication method. At the concentration place of multiple surname man, average surname man harvest is estimated with the division method. The addition and subtraction of negative numbers have the following examples: "-1 + (-1) = -2", "-2 - (-1) = - (2 - 1) = -1". According to reason, or inference and induction logic, because "A x 0 = 0", so "A x (-1)" is less than "0". In other words, because the multiplication formulas of a negative number and a positive number or zero are "-1 x 1 = -1, -1 x 0 = 0, -1 / 0 = negative infinity, 0.1 x 0.1 = 0.01, 0 x 0 = 0, 0 / 0 = indefinite number (no solution)", also because a negative number is less than a positive number, therefore, "-1 x -1 < 0, -1 / -1 < 0", this is negative number, or no solution. In other words, for positive numbers "A" and "B", we have "-A x -B < 0, -A / (-B) < 0".
按照現有數學書中負數(-A)和(-B)乘除法公式“-A x -B = A x B, -A / -B = A / B”﹐因為從二個到多個負數的乘除法的結果在正負二極之間跳躍﹐不符合自然相連性和繼承性規律﹐所以現有負數乘除法公式是錯誤的。按照上節乘法的相同數加法本質﹐除法的平均值本質﹐這兩個公式沒有真正實用的應用實例﹐即不是真實的﹐所以﹐這二個公式既不是實數學﹐又不是真理﹐更不是正義意識公式﹐而是錯誤的負義意識公式。
According to existing multiplication or division formulas for negative numbers (-A) and (-B) "-A x -B = A x B, -A / -B = A / B" in mathematics books, because the multiplication or division of from two to multiple negative numbers give result that jumps between positive extreme and negative extreme, this does not accord with natural laws of continuity and inheritance, so the existing negative number multiplication or division formulae are wrong. According to the essence of multiplication as addition of same number, the essence of division as average value in the above paragraph, these two formulae do not have any true real example of application, i.e., they are not real, so these two formulas are neither real mathematics nor truth, nor formulae of justice rights ideology, but, wrong formulae of negative rights ideology.
按照現有數學﹐在加法或減(方言“gang - 講”)法運算中﹐可以從各項中取出負號。求差減法如果以比較正的數為參考點﹐即被減數﹐就避免“-(-1)”運算。等式雙邊可以同時放棄負號。因而﹐不需要運用負數乘除法公式。一些負數是減號假象﹑數據抽象誤解﹑或者原點定得太高﹐例如可以循環利用的屎尿和垃圾水被某些人誤解和誤用為負數﹐水平線以下位置可能標記為負數﹐相反﹐負義金錢武器可能被誤解為正數。把一切物質都標為正數價格﹐和把物品的制造時間和費用變成正數價格﹐是可疑的﹐或者錯誤的。上述錯誤公式可能使人忽視數據的符號﹐不及時改正負義。選擇適當的原點能夠保證正數運算﹐在結果分析時處理負數(參考攝氏零度反映水的結冰性質變化﹐熱力學絕對溫度絕對保證正數運算﹐華氏溫度的原點是攝氏“-17.7777”﹐在很低的溫度下﹐氣體冷卻變成固體﹐熱力學公式不適用﹐從地球繞太陽運行的觀點看﹐攝氏零度和華氏零度的差別是缺乏陽光的時期和範圍﹑大地熱量和可能的冷氣流動的差別)。假若通過降低原點﹐把二負數化為二正數﹐那麼﹐加乘除三法運算的結果都是正數﹐所以二負數“加乘除”三法的結果都是負數。上述從正反假三方面靈活地改正了“負數乘除負數等于正數”的數學公式錯誤。負數乘除負數等于負數﹐即“-1 x -1 = -1, -1 / -1 = -1”﹐必須檢查各個負數符號的真假。
According to present mathematics, in the addition or subtraction operation, the negative signs may be taken out of all the terms. In the number subtraction to find the difference, if the more positive number is used as the reference i.e. the minuend, then the "-(-1)" calculation is avoided. Both sides of an equation may abandon the negative signs simultaneously. Therefore, there is no need to use the negative numbers multiplication or division formulas. Some negative numbers are the false image of the subtraction sign, data abstraction misunderstanding, or the origin point being set too high, e.g., the excrement and garbage water that can be put into cyclic utilization are misunderstood and used by some as negative number, position under water horizon may be marked as negative number, on the contrary, metal money weapon of negative rights may be misunderstood as positive number. To label all matter as positive price, and to change product making time and cost into positive price, are doubtful or wrong. The above wrong formulae may make one ignore the sign of datum, not to correct negative rights on time. To select the proper origin can ensure calculation with positive numbers, then dealing with negative numbers in the result analysis (ref. zero degree Celsius reflects fresh water freezing property change, thermo dynamics absolute temperature ensures absolutely positive number calculation, Fahrenheit temperature origin is Celsius "-17.7777", under very low temperature gas cools down to change to solid and thermodynamics formulae do not apply, from earth revolution around the sun point of view, Celsius zero and Fahrenheit zero difference is one of duration and extent of sunshine absence, ground mass heat as well as possible cold air flow). Supposing by lowering the origin, two negative numbers are changed into two positive numbers, then, three operations of addition, multiplication and division all result in positive numbers, so, for two negative numbers, three operations of "addition, multiplication and division" should all result in negative numbers. These have, from positive to negative to fake three directions with flexibility, corrected the mathematics mistaking error that "負數乘除負數等于正數 a negative number multiplied with or divided by a negative number equals a positive number". Two negative number multiplication and division equal to, i.e., "-1 x -1 = -1, -1 / -1 = -1", one must check if the sign of each number is true or false.
在岩石力學中﹐壓應力規定為正數﹐拉應力規定為負數。假若有拉應力乘拉應力的問題﹐其結果只能是拉應力的函數﹐而不是壓應力函數﹔對于除法﹐拉應力和抗拉強度的比例仍然是拉應力﹐而不是壓應力。在一些條件下﹐壓力波和拉力波之間能互相轉變。
In rock mechanics, compressive stress is defined to be positive, tensile stress is defined to be negative. If there is tensile stress multiplied by tensile stress question, the result can only be a function of tensile stress, not compressive stress; as for division, tensile stress over tensile strength ratio is still function of tensile stress, not compressive stress. Under some condition, compressive wave and tensile wave can transform into each other.
KEYWORDS
Mining, science, spring, negative numbers, compressive stress, tensile stress, normalized stress.