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Calculus 4E Lesson 2

Space, time, and numbers

QuestionAnswer
Plato's challenge is to MATHEMATICALLY describe the apparently chaotic motion of the ______________________. heavens
Heraclitus believed that _____________________ changes. everything
Parmenides believed that _____________________ changes and that the very concept of change is incoherent. nothing
Zeno's paradox was to suggest that __________________ simply cannot occur. motion
Zeno's paradox rightly pointed out that motion is a difficult concept to analyze or define and that we need to be able to precisely DEFINE motion.
Aristotle said that "Ignorance of motion is ignorance of nature."
The Greeks used the word "motion" to describe ________ change. any
Zeno made the assumption that distances are infinitely _____________________, they can be divided in half _________________. divisible . . . forever
A genuine mathematical line has no _______________ or __________________. The lines we draw or imagine are just copies of the true FORM of a line. breadth (or) thickness
All lines, regardless of how long they are, contain an _____________________ number of points. infinite
When we say a line is continuous, we mean it has no __________, no empty places. gaps
Points and lines are the most basic entities of ___________________. geometry
Geometry can be called "the science of __________________." space
The number line unites the realm of ____________________ and the realm of ____________________. number (and) points
By "numerical address," we mean that every point on a ___________________ ____________ is paired with its own personal number. number line
Numbers and lines share the strangeness associated with ___________________ and _______________. continuity (and) infinity
The similarities between the structures of mathematics and the physical universe provide evidence for a Creator because the user-friendliness of the universe indicates that there is SOMEONE who wants us to know about HIS creation.
Created by: MrsHough
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