Which number is bigger?

  • #1

Main Question or Discussion Point

hi...how can i tell which number is larger just from using logic?

for example a question says "which is larger 2^1000 or 500!?" the answer is 500! and the hint is: just compare the 500 factors appearing in each expression. i don't understand the hint but more importantly, i'm just not seeing the logic part of it.

thanks,
barneygumble742
 

Answers and Replies

  • #2
selfAdjoint
Staff Emeritus
Gold Member
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Are you sure you copied this right? Because 2^1000 > 1000^100 > 500.
 
  • #3
that's not 500 exclamation point. it's 500 factorial. should i have used a different notation?
 
  • #4
1,356
2
make 2^1000 into 500 factors and compare the factors is what the hint is suggesting
2^1000=(2^2)^500. and then compare it to 500 factors of 500!
 

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