Can the number 1 be squared infinitely many times?

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SUMMARY

The forum discussion centers on the mathematical implications of squaring the number 1 in the context of special relativity, specifically regarding the equation for the relativity of simultaneity. Users debate the legitimacy of introducing the speed of light constant, c, in various forms, particularly when c is set to 1. The consensus is that while one can square 1 infinitely, the algebraic manipulation involving c must remain dimensionally consistent. The discussion highlights the importance of maintaining clarity in mathematical expressions to avoid confusion, especially for students learning relativity.

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  • Understanding of special relativity concepts, particularly the relativity of simultaneity.
  • Familiarity with algebraic manipulation involving constants and dimensional analysis.
  • Knowledge of the speed of light constant (c) and its role in physics equations.
  • Basic comprehension of Minkowski space and pseudo-Riemannian geometry.
NEXT STEPS
  • Study the implications of setting c=1 in special relativity and its effects on dimensional analysis.
  • Learn about the derivation and significance of the equation for the relativity of simultaneity.
  • Explore the concept of flight time difference in the context of light travel in different frames of reference.
  • Review algebraic techniques for manipulating fractions and constants in physics equations.
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Students of physics, particularly those studying special relativity, educators teaching relativity concepts, and anyone interested in the mathematical foundations of physics.

  • #31
I always thought the brackets are interchangable in the 2 examples. Do you have a vid or article that shows the difference?
 
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  • #32
rgtr said:
I always thought the brackets are interchangable in the 2 examples. Do you have a vid or article that shows the difference?
The parentheses tell the reader the order of execution of the operators.
a/(b/c) says to do b/c first, so a/(b/c)=(ac)/b, whereas (a/b)/c=a/(bc).
In LaTeX parentheses can be omitted when the font size makes it clear.
##\frac a{\frac bc}## implies ##\frac a{(\frac bc)}## whereas ##\frac {\frac ab}c## implies ##\frac {(\frac ab)}c##.
 
  • #33
rgtr said:
I always thought the brackets are interchangable in the 2 examples. Do you have a vid or article that shows the difference?
Division is not associative. Neither is subtraction.
##(a/b)/c\ne a/(b/c)##

Addition and multiplication are associative.
 
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