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[20] [21] The acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction, [22] is common in the United States [23] and France. [24] Sometimes the letters are expanded into words of a mnemonic sentence such as "Please Excuse My Dear Aunt Sally". [ 25 ]
Socratic questioning (or Socratic maieutics) [1] is an educational method named after Socrates that focuses on discovering answers by asking questions of students. According to Plato, Socrates believed that "the disciplined practice of thoughtful questioning enables the scholar/student to examine ideas and be able to determine the validity of those ideas". [2]
But as a general rule, if a series of operation contains a mix of additions and subtractions, then doing it from right to left will likely give you the wrong answer. So forcing the "left to right" rule will guarantee the right answer in the general case. Dhrm77 10:49, 23 August 2023 (UTC) I've added another reference.
The earliest written mathematics likely began with tally marks, where each mark represented one unit, carved into wood or stone.An example of early counting is the Ishango bone, found near the Nile and dating back over 20,000 years ago, which is thought to show a six-month lunar calendar. [6]
From around 2500 BC onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems. The earliest traces of Babylonian numerals also date back to this period. [8] Babylonian mathematics has been reconstructed from more than 400 clay tablets unearthed since the 1850s. [9]
The "nine dots" puzzle. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen.
Video: Keys pressed for calculating eight times six on a HP-32SII (employing RPN) from 1991. Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which operators follow their operands, in contrast to prefix or Polish notation (PN), in which operators precede their operands.
A key point is that the extra operations do not add information, but follow uniquely from the usual definition of a group. Although the usual definition did not uniquely specify the identity element e, an easy exercise shows that it is unique, as is the inverse of each element. The universal algebra point of view is well adapted to category theory.