By Clark G. L.

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Extra resources for Correctness of the definition of a PD operator

Sample text

Strictly speaking, we should include them when writing a long list of equals signs. An example of this will be given in Chapter 21. If you are unsure how to use =⇒ or ⇐⇒, then consult Chapters 7 and 9. Use common symbols and notation Some symbols are given a common fixed meaning. The prime example of this is π , which represents the circumference of a circle divided by its diameter. g. it is often used for a projection map (since π represents p, and p is the first letter of projection). It is also used for the fundamental group of a space in algebraic topology.

If you are unsure where to use it, then say the sentence out loud with the symbol ⇒ replaced by ‘implies’ or ‘implies that’ as often this will help. Similar problems are found with the symbol ⇐⇒, the biconditional; see Chapter 9. This is used to assert that two statements are equivalent. Strictly speaking, we should include them when writing a long list of equals signs. An example of this will be given in Chapter 21. If you are unsure how to use =⇒ or ⇐⇒, then consult Chapters 7 and 9. Use common symbols and notation Some symbols are given a common fixed meaning.

Draw a picture The human mind is very good at working with images. Pictures are excellent for developing intuition about a problem and subsequently suggesting a solution to it. In fact, a diagram is often essential in problems from geometry or physics. In the case of problem (ii) drawing a Venn diagram is very illuminating. Devising a plan 45 Think about a similar problem As stated earlier, the way to become good at solving problems is to solve problems. Similar problems often have similar solutions, so consider problems with similar assumptions or conclusions that you have solved before and see if the same method will work.