Taking a power of 2 or power of d

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In summary, the conversation discusses the concept of taking "power of 2" or "power of d" in a game, referring to the use of counters or moves on a board. The question arises whether 2^0 counts as a power of 2 and if irrational powers of 2 also count. It is generally considered that 1 is a power of 2, but it can be excluded like 0 is sometimes excluded from the set of natural numbers. The use of \neq in latex is also mentioned.
  • #1
Trail_Builder
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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 [tex]2^{n}[/tex] 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 [tex]2^{0} = 1[/tex] counted as a power of 2??

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

so, does [tex]2^{0} = 1[/tex] 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 [tex]2^{\frac{3}{2}}[/tex]. I'm guessing it still does, just need to check :D
 
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  • #2
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 [tex]2^{3/2}[/tex] a power of 2.

Not equals is \neq in latex. :) [tex]1\neq 2[/tex]
 
  • #3
thnx dude :D
 

1. What does it mean to take a power of 2?

Taking a power of 2 means raising the number 2 to a certain exponent. For example, 2 to the power of 3 would be 2 x 2 x 2, which equals 8.

2. How do you compute a power of 2?

To compute a power of 2, you can use the formula 2^x where x is the desired exponent. You can also use a calculator or manually multiply 2 by itself the specified number of times.

3. What are some real-world applications of taking powers of 2?

Taking powers of 2 is commonly used in computer science and digital technology, as computers use binary code which is based on the powers of 2. It is also used in finance and economics for compounding interest calculations.

4. What is the significance of taking a power of 2?

Taking a power of 2 can result in very large numbers, which can have practical applications in fields such as cryptography and data encryption. It is also used in calculating probabilities and in geometric and exponential growth models.

5. How is taking a power of 2 different from taking a power of a different number?

The main difference is that powers of 2 are commonly used in computer science and digital technology due to the binary system, while powers of other numbers may have different applications in various fields of science and mathematics. Additionally, the pattern of powers of 2 is unique, as each power is double the previous power, while other numbers may have different growth patterns.

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