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heff001

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In 'AN INTRODUCTION TO SET THEORY' by Professor William A. R. Weiss, the following symbols are applied to the snippet below:

...

The collection of formulas of set theory is defined as follows:

1. An atomic formula is a formula.

2. If

...

I am new to Set Theory and my 'greenhorn' question really is about the use of these specific symbols here (I understand the Basics). In his book, has he assigned the Greek symbols shown above and states

Never mind - see

http://www.mathacademy.com/pr/prime/articles/greek/index.asp

The Greek Alphabet

Mathematics requires a large number of symbols to stand for abstract objects, such as numbers, sets, functions, and spaces, so the use of Greek letters was introduced long ago to provide a collection of useful symbols to supplement the usual Roman letters.

To us these symbols may seem quite foreign, and they are difficult to become familiar with. However, at the time they were introduced, most scholars had been taught at least some Latin and Greek during their education, so the letters did not seem nearly so strange to them as they do to us. Since then, each new generation of mathematicians has just gotten used to using them.

The Greek alphabet contains lower-case letters that are used more often than the upper-case letters, but the latter are used often enough. The lower-case letters are most often used for variables, such as angles and complex numbers, and for functions and formulas, while the upper-case letters more commonly stand for sets and spaces, and sometimes for repeated arithmetic operations such as adding and multiplying (see Sigma and Pi). In any particular textbook or paper, the way in which these symbols should be interpreted should generally be clear from the context and definitions.

...

The collection of formulas of set theory is defined as follows:

1. An atomic formula is a formula.

2. If

**ϕ**and**Ψ**are formulas, then (**ϕ**^**Ψ**) is also a formula....

I am new to Set Theory and my 'greenhorn' question really is about the use of these specific symbols here (I understand the Basics). In his book, has he assigned the Greek symbols shown above and states

*we have now specified a 'language' of set theory*. Can someone please explain what the bolded Capital Phi**ϕ**symbol and**Ψ**symbol represent specifically in the field of Set Theory, or has he just applied them in his book purely as formula symbols as 'his' specification of set theory 'language'.Never mind - see

http://www.mathacademy.com/pr/prime/articles/greek/index.asp

The Greek Alphabet

Mathematics requires a large number of symbols to stand for abstract objects, such as numbers, sets, functions, and spaces, so the use of Greek letters was introduced long ago to provide a collection of useful symbols to supplement the usual Roman letters.

To us these symbols may seem quite foreign, and they are difficult to become familiar with. However, at the time they were introduced, most scholars had been taught at least some Latin and Greek during their education, so the letters did not seem nearly so strange to them as they do to us. Since then, each new generation of mathematicians has just gotten used to using them.

The Greek alphabet contains lower-case letters that are used more often than the upper-case letters, but the latter are used often enough. The lower-case letters are most often used for variables, such as angles and complex numbers, and for functions and formulas, while the upper-case letters more commonly stand for sets and spaces, and sometimes for repeated arithmetic operations such as adding and multiplying (see Sigma and Pi). In any particular textbook or paper, the way in which these symbols should be interpreted should generally be clear from the context and definitions.

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