Math or Maths

If you ever got into contact with the word "mathematics", you have certainly also seen at least one of the nouns from the pair "math" and "maths". But which one is correct? How do you spell it shortly, "math" or "maths"? Let's take a quick look upon this linguistic confusion to make sure you get it right.

Math vs. Maths

Both "math" and "maths" are abbreviations for the word "mathematics", the complex science that studies numbers and shapes. We can't claim that any of these abbreviated forms is right or wrong, because they are just shorter versions for the full noun ("mathematics"). Whether you prefer adding the last "s" or not is a matter of personal choice and culture, according to how you've been educated in school and how you have seen it spelled more frequently.

There are, anyway, some statistics that show how often "math" and "maths" are used. It turns out that, just as it happens for other pairs of words that differ through only one letter, the frequency of use regarding the different abbreviations differs from British to Americans. Here's how:

Is “math” or “maths” the correct word to use as the shortened or colloquial form of the word mathematics? The answer is that it depends on where you are.

To North American speakers of English, the word to use is “math”, as in “I majored in math”, and “maths” would sound wrong. Speakers of British English, however, would always say “maths”, as in “I took a degree in maths”. They would never say “math”.

There are logical arguments for both spellings. The word “mathematics” can be considered as a singular and as a plural noun. Both the Oxford and the Merriam-Webster dictionaries say the word is plural – hence the s on the end – but also that it is usually used as if it was a singular noun. So, most people would say “mathematics is my best subject” and not “mathematics are my best subject”. The shortened form “maths”, then, makes sense because the word is still a plural noun and so should still have the “s” on the end. On the other hand, it could be argued, “math” makes sense because it seems wrong to remove the letters “ematic” from the middle of the word and leave the final “s”.

When do we use "maths"?

"Maths" is the abbreviation preferred by the British. In the UK, they say that "mathematics" ends in "s" and so should its short form. It's more likely that if you ask a British person, they would tell you they prefer "maths" as they have seen it spelled like this all the time.

When do we use "math"?

"Math" is preferred by the Americans, not only because they usually go for the shorter forms, but also because they consider "mathematics" is a mass noun that takes singular verbs and should, therefore, be abbreviated without the "s" in the end.

Conclusion

"Math" and "maths" are not complete words on their own and. As abbreviations, they can't be considered wrong or right. Choosing a form will be partially influenced by your personal choice and logic, and partially by the region where you've learned to spell it. British use "maths" more often and Americans prefer "math", but this does not define any rule for correct spelling.

******************

*Used for education purpose

Content source : 

various websites and wikipedia ..

Collected and organised :

Sathiskumar Education

******************

Types of set

Types of set

There are many types of set in the set theory:

1. Singleton set
If a set contains only one element it is called to be a singleton set.
Hence the set given by {1}, {0}, {a} are all consisting of only one element and therefore are singleton sets.
2. Finite Set
A set consisting of a natural number of objects, i.e. in which number element is finite is said to be a finite set. Consider the sets
A = { 5, 7, 9, 11} and B = { 4 , 8 , 16, 32, 64, 128}
Obviously, A, B contain a finite number of elements, i.e. 4 objects in A and 6 in B. Thus they are finite sets.
3. Infinite set
If the number of elements in a set is finite, the set is said to be an infinite set.
Thus the set of all natural number is given by N = { 1, 2, 3, ...} is an infinite set. Similarly the set of all rational number between ) and 1 given by
A = {x:x E Q, 0 <x<1} is an infinite set.
4. Equal set
Two set A and B consisting of the same elements are said to be equal sets. In other words, if an element of the set A sets the set A and B are called equal i.e. A = B.
5. Null set/ empty set
A null set or an empty set is a valid set with no member.
A = { } / phie cardinality of A is 0.
There is two popular representation either empty curly braces { } or a special symbol phie. This A is a set which has null set inside it.
6. Subset
A subset A is said to be subset of B if every elements which belongs to A also belongs to B.

    A = { 1, 2, 3}
    B = { 1, 2, 3, 4}
    A subset of B.

7. Proper set
A set is said to be a proper subset of B if A is a subset of B, A is not equal to B or A is a subset of B but B contains at least one element which does not belong to A.
8. Improper set
Set A is called an improper subset of B if and Only if A = B. Every set is an improper subset of itself.
9. Power set
Power set of a set is defined as a set of every possible subset. If the cardinality of A is n than Cardinality of power set is 2^n as every element has two options either to belong to a subset or not.
10. Universal set
Any set which is a superset of all the sets under consideration is said to be universal set and is either denoted by omega or S or U.

    Let  A = {1, 2, 3}
    C = { 0, 1} then we can take
    S = {0, 1, 2, 3, 4, 5, 6, 7, 8}