Variables definition in Euler's introduction to analysis

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SUMMARY

Euler defines a variable as "an indeterminate or universal quantity, which includes within itself all completely determined values." This indicates that a variable can represent any numerical value, encompassing both constants and complex values. The term "completely determined values" refers to constants established earlier in the text. Furthermore, Euler emphasizes that a variable remains undetermined until a specific value is assigned through computation.

PREREQUISITES
  • Understanding of mathematical variables and constants
  • Familiarity with Euler's works, particularly his definitions in analysis
  • Basic knowledge of complex numbers
  • Ability to interpret historical mathematical texts
NEXT STEPS
  • Study Euler's "Introduction to Analysis" for deeper insights into his definitions
  • Explore the concept of variables in modern mathematics
  • Research the role of constants in mathematical equations
  • Learn about the computation methods for assigning values to variables
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Mathematicians, educators, students of mathematics, and anyone interested in the foundational concepts of analysis and variable theory.

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In his book, Euler gives the definition of a variable to be : "A variable quantity is an indeterminate or universal quantity, which includes within itself all completely determined values." What does he mean exactly in the last part of the sentence?
 
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If I interpret the German original correctly, he means that a variable can represent any value, and by value he means a number.

eulervariable.jpg


The "completely determined values" are the constants defined in the preceding paragraph.

In the following page he explains that a variable has an undetermined value, until by computation you can assign it a determined value (including complex values).

eulervariable2.jpg


http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN379242303&DMDID=DMDLOG_0007
 
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