But things really got going in Middle English —English as it existed between the 12th and 15th centuries. In texts from that period the OED notes the following spellings:. The winner, of course, is forty , nearly the last of the bunch.
The logical Middle English relic fourty , hiding most of the way down that long list, lasted until the 18th century, when for reasons unknown it fell out of use.
Sometimes that's just how it goes in English. Oxford University Press. Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free!
Log in Sign Up. Usage Notes Is it 'Forty'? Or 'Fourty'? This is usage. What to Know Forty is the proper spelling of the number in all English variants despite the fact that four contains a u. More Words At Play. For example, some musicians are singers and some play an instrument. The union of two sets A and B consists of all elements belonging to A or to B. Elements belonging to both set belong to the union.
Continuing with the example of singers and instrumentalists:. Here the elements 6 and 12 are in both sets A and B. Another way to define disjoint sets is to say that their intersection is the empty set,. Let A and B be subsets of a suitable universal set E. Here is the Venn diagram of the situation. The region inside the circle represents the set A , so we place the numbers 1, 3, 5, 7 and 9 inside the circle.
Outside the circle, we place the other numbers 0, 2, 4, 6, 8 and 10 that are not in A. When we know that two sets are disjoint, we represent them by circles that do not intersect.
For example, let. Then P and Q are disjoint, as illustrated in the Venn diagram below. Solving problems using a Venn diagram. Before solving problems with Venn diagrams, we need to work out how to keep count of the elements of overlapping sets. The upper diagram to the right shows two sets A and B inside a universal set E , where. The lower diagram to the right shows only the number of elements in each of the four regions. In the diagram to the right,.
Many counting problems can be solved by identifying the sets involved, then drawing up a Venn diagram to keep track of the numbers in the different regions of the diagram. A travel agent surveyed people to find out how many of them had visited the cities of Melbourne and Brisbane. Thirty-one people had visited Melbourne, 26 people had been to Brisbane, and 12 people had visited both cities.
Draw a Venn diagram to find the number of people who had visited:. Let M be the set of people who had visited Melbourne, and let B be the set of people who had visited Brisbane. Let the universal set E be the set of people surveyed. Twenty-four people go on holidays. If 15 go swimming, 12 go fishing, and 6 do neither, how many go swimming and fishing?
Draw a Venn diagram and fill in the number of people in all four regions. In a certain school, there are pupils in Year 7. One hundred and ten pupils study French, 88 study German and 65 study Indonesian. Forty pupils study both French and German, 38 study German and German only. Find the number of pupils who study:. The examples in this module have shown how useful sets and Venn diagrams are in counting problems.
Such problems will continue to present themselves throughout secondary school. The language of sets is also useful for understanding the relationships between objects of different types. For example, we have met various sorts of numbers, and we can summarise some of our knowledge very concisely by writing.
The relationships amongst types of special quadrilaterals is more complicated. Here are some statements about them. That is, the set of convex kites and the set of non-convex kites are disjoint, but their union is the set of all kites.
It is far easier to talk about probability using the language of sets. The set of all outcomes is called the sample space , a subset of the sample space is called an event. Thus when we throw three coins, we can take the sample space as the set. A Venn diagram is the best way to sort out the relationship between the two events E and F.
We can then conclude that. Consequently we mostly avoid set notation altogether, and use instead less rigorous language,. Speaking about the condition rather than about the set, however, can confuse some students, and it is often useful to demonstrate the set theory ideas lying behind the abbreviated notation.
In set-builder notation, the solutions to the two inequalities are. At school, however, we simply write the solutions to the two inequalities as the conditions alone,. There are many similar situations where the more precise language of sets may help to clarify the solutions of equations and inequalities when difficulties are raised during discussions. Counting problems go back to ancient times. In the hierarchy of infinities that he discovered, the infinity of the whole numbers is the smallest type of infinity, and is the same as the infinity of the integers and of the rational numbers.
He was able to prove, quite simply, that the infinity of the real numbers is very much larger, and that the infinity of functions is much larger again. The topic is quite suitable as extension work at school, and the basic ideas have been presented in some details in Appendix 2 of the Module The Real Numbers. But, fortnight is very useful, which is why it still has currency in British English and other forms of English around the world.
Consider the words biweekly and bimonthly. Enter fortnightly , which offers a welcome workaround to the ambiguity of biweekly and bimonthly. If your doctor tells you to take a medication fortnightly , you know you should take it every two weeks.
If a teacher says you will have fortnightly quizzes in class … we think you get the idea. The answer to this question all comes down how variable English spelling has been over centuries. Fortnight was spelled fourtenight in Middle English along with furtenight , fowrtnight , and many other forms. Over the past years, these variant spellings have fought it out, and forty , introduced in the 16th century, has won the day. For the moment. OK, we do see a lot of searches for Fortnite on Dictionary.
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