Taking a power of 2 or power of d

  • Thread starter Thread starter Trail_Builder
  • Start date Start date
  • Tags Tags
    Power
AI Thread Summary
The discussion centers on the definition of "power of 2" in mathematical problems, specifically whether 2^0 = 1 should be included as a power of 2. It is noted that while 1 is generally accepted as a power of 2, its inclusion can complicate problem-solving. The conversation also touches on whether irrational powers, like 2^(3/2), qualify as powers of 2, with the consensus leaning towards inclusion. The definition of natural numbers is mentioned, highlighting that 0 is sometimes excluded from this set. Ultimately, the conversation emphasizes the flexibility in defining powers of 2 based on context.
Trail_Builder
Messages
148
Reaction score
0
taking a "power of 2" or "power of d"

i was trying some of the problem in a few of the books i have and on more than one occasion cam across a question that referred to people in a game taking a "power of 2" or "power of d" or whatever. referring to taking counters or equivalent thing, such as moves on a board or whatever (so intergers only).

now, what i was wondering is, naturally, one would assume in 2^{n} for a power of 2. n would be a natural number and equal to or bigger than 1. (whats the 'not equal to' sign in latex :S).

however, after doing the problem assuming this, i suddenly wondered if 2^{0} = 1 counted as a power of 2??

this is cause would cause complications in solving the problem but nothing too problematic.

so, does 2^{0} = 1 count? I am guessing it does, but just need to check.

also, if the problem doesn't specifically revolve around integers, would an irrational power of 2 still count as a "power of 2"? such as 2^{\frac{3}{2}}. I'm guessing it still does, just need to check :D
 
Mathematics news on Phys.org
1 is generally considered a power of 2, but it's sometimes excluded (just like 0 is sometimes excluded from the set of natural numbers). Just disregard it if it creates obvious troubles. Every positive number can be written as a power of 2 to a real number, so it would be meaningless to call 2^{3/2} a power of 2.

Not equals is \neq in latex. :) 1\neq 2
 
thnx dude :D
 
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
Back
Top