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:↳ [[Math_Squad_infinity_mhossain_S13|To Infinity and Beyond. Introduction]] | :↳ [[Math_Squad_infinity_mhossain_S13|To Infinity and Beyond. Introduction]] | ||
::↳ [[Math_Squad_infinity_review_of_set_theory__mhossain_S13|Review of Set Theory]] | ::↳ [[Math_Squad_infinity_review_of_set_theory__mhossain_S13|Review of Set Theory]] | ||
| − | :::↳ Functions | + | :::↳ [[Math_Squad_infinity_review_of_set_theory_function_mhossain_S13|Functions]] |
| − | :::↳ Countability | + | :::↳ [[Math_Squad_infinity_review_of_set_theory_countablity_mhossain_S13|Countability]] |
| − | :::↳ Cardinality | + | :::↳ [[Math_Squad_infinity_review_of_set_theory_cardinality_mhossain_S13|Cardinality]] |
| − | ::↳ Hilbert's Grand Hotel | + | ::↳ [[Math_Squad_infinity_Hilbert_hotel_mhossain_S13|Hilbert's Grand Hotel]] |
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| − | Georg Cantor called a set a collection of objects. This simple idea was so profound that it has become the foundation of every branch of mathematics. Cantor's theories became an important tool that allowed mathematicians to precisely define concepts such as real numbers, points in space, and continuous functions. In addition, Cantor's theory of sets provided | + | Georg Cantor called a set a collection of objects. This simple idea was so profound that it has become the foundation of every branch of mathematics. Cantor's theories became an important tool that allowed mathematicians to precisely define concepts such as real numbers, points in space, and continuous functions. In addition, Cantor's theory of sets provided startling new insight into the nature of infinity among which was the fact that some infinite magnitudes are larger than others. We will explore this idea more deeply in this section of the tutorial by studying the following topics |
* [[Math_Squad_infinity_review_of_set_theory_function_mhossain_S13|Functions]] | * [[Math_Squad_infinity_review_of_set_theory_function_mhossain_S13|Functions]] | ||
| − | * Countability | + | * [[Math_Squad_infinity_review_of_set_theory_countablity_mhossain_S13|Countability]] |
| − | * Cardinality | + | * [[Math_Squad_infinity_review_of_set_theory_cardinality_mhossain_S13|Cardinality]] |
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== References == | == References == | ||
| − | * Lewin | + | * J. Lewin, "Elements of Set Theory" in An Interactive Introduction to Mathematical Analysis, Cambridge, UK: Cambridge University Press. 2003 ch. 4, pp 50-51 |
| + | |||
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Latest revision as of 19:23, 24 May 2013
- ↳ To Infinity and Beyond. Introduction
- ↳ Review of Set Theory
- ↳ Functions
- ↳ Countability
- ↳ Cardinality
- ↳ Hilbert's Grand Hotel
- ↳ Review of Set Theory
To Infinity and Beyond
A Review of Set Theory
by Maliha Hossain, proud member of the Math Squad
Georg Cantor called a set a collection of objects. This simple idea was so profound that it has become the foundation of every branch of mathematics. Cantor's theories became an important tool that allowed mathematicians to precisely define concepts such as real numbers, points in space, and continuous functions. In addition, Cantor's theory of sets provided startling new insight into the nature of infinity among which was the fact that some infinite magnitudes are larger than others. We will explore this idea more deeply in this section of the tutorial by studying the following topics
References
- J. Lewin, "Elements of Set Theory" in An Interactive Introduction to Mathematical Analysis, Cambridge, UK: Cambridge University Press. 2003 ch. 4, pp 50-51
Questions and comments
If you have any questions, comments, etc. please post them below:
- Comment / question 1
