Abstract Algebra IBL Wiki

User Tools

Site Tools

Trace:
elements_of_style_for_proofs

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
elements_of_style_for_proofs [2016/04/19 20:35]
bmwoodruff 		elements_of_style_for_proofs [2016/04/19 20:36] (current)
bmwoodruff
Line 20: Line 20:
 </html> Some complete sentences can be written purely in mathematical symbols, such as equations (e.g., $a^3=b^{-1}$), inequalities (e.g., $x<5$), and other relations (like $5\big|10$ or $7\in\mathbb{Z}$). These statements usually express a relationship between two mathematical \emph{objects}, like numbers or sets.  However, it is considered bad style to begin a sentence with symbols.  A common phrase to use to avoid starting a sentence with mathematical symbols is "We see that..." </html> Some complete sentences can be written purely in mathematical symbols, such as equations (e.g., $a^3=b^{-1}$), inequalities (e.g., $x<5$), and other relations (like $5\big|10$ or $7\in\mathbb{Z}$). These statements usually express a relationship between two mathematical \emph{objects}, like numbers or sets.  However, it is considered bad style to begin a sentence with symbols.  A common phrase to use to avoid starting a sentence with mathematical symbols is "We see that..."
   - **Show the logical connections among your sentences.** Use phrases like "Therefore" or "because" or "if$\ldots$, then$\ldots$" or "if and only if" to connect your sentences.   - **Show the logical connections among your sentences.** Use phrases like "Therefore" or "because" or "if$\ldots$, then$\ldots$" or "if and only if" to connect your sentences.
-  - **Use paragraphs to organize your work into logical chunks. If every sentence starts a new paragraph, then you are not logical organizing your work.  Similarly, if you have a long proof and all your sentences are in a single paragraph, you are not logically organizing your work. Use paragraphs to put structure and order to your work. +  - **Use paragraphs to organize your work into logical chunks.** If every sentence starts a new paragraph, then you are not logical organizing your work.  Similarly, if you have a long proof and all your sentences are in a single paragraph, you are not logically organizing your work. Use paragraphs to put structure and order to your work. 
   - **Know the difference between statements and objects.** A mathematical object is a //thing//, a noun, such as a group, an element, a vector space, a number, an ordered pair, etc. Objects either exist or don't exist. Statements, on the other hand, are mathematical //sentences//:  they can be true or false.<html>   - **Know the difference between statements and objects.** A mathematical object is a //thing//, a noun, such as a group, an element, a vector space, a number, an ordered pair, etc. Objects either exist or don't exist. Statements, on the other hand, are mathematical //sentences//:  they can be true or false.<html>
 <br><br> <br><br>
elements_of_style_for_proofs.txt ยท Last modified: 2016/04/19 20:36 by bmwoodruff

Page Tools

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
CC Attribution-Share Alike 4.0 International Donate Powered by PHP Valid HTML5 Valid CSS Driven by DokuWiki