Clarifying Mathematical Confusion: The Truth About 1010101010

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Discussion Overview

The discussion revolves around the mathematical interpretation of the expression 1010101010 and its equivalence to (((1010)10)10)10. Participants explore the order of operations in exponentiation and the implications of large numbers in relation to the observable universe.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions whether 1010101010 equals (((1010)10)10)10, suggesting a misunderstanding of the order of operations.
  • Another participant explains that the correct approach is to work down through the exponents, providing an example with 10^{2^3} to illustrate the difference in results based on the order of operations.
  • A third participant attempts to express 1010101010 in terms of its magnitude, suggesting it is an extremely large number, and questions the feasibility of calculating such a number given the estimated number of atoms in the observable universe.
  • A later reply challenges the relevance of the number of atoms in the universe to the concept of calculating large numbers, prompting further clarification.

Areas of Agreement / Disagreement

Participants generally agree on the importance of the order of operations in exponentiation, but there is disagreement regarding the relevance of the number of atoms in the universe to the calculation of large numbers.

Contextual Notes

There are unresolved assumptions regarding the definitions of "calculated" and the implications of large numbers in practical terms.

Nick666
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My math is rusty so please tell me

1010101010[/size] does not equal (((1010)10)10)10 , right ?
 
Last edited:
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Right. You have to work your way down rather than work you way up the chain of exponents.

Here's a simpler example:
[tex]10^{2^3}[/tex]

If you worked your way up through the exponents, this would be (102)3 = 106
If you work your way down, you get 10(23) = 108
 
Allright, so here we go

=101010100[/size]

=10101followed by 100 zeros[/size]

=101followed by 10000 trillion trillion trillion trillion trillion trillion trillion trillion of zeros [/size][/color]

=...

My question is, and maybe this should be moved on another forum,

Can the number be calculated ? I mean the observable universe has like "1followed by ~80 zeros" atoms , so a number like the one above can't be calculated right ? I can't imagine a machinery in this universe even operating with the number written in red... What about a quantum computer ?
 
What do you mean by "calculated"? I honestly don't see how the number of atoms in the observable universe has anything to do with calculating a number.
 

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