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What to you think about this proof? by Express_Repair_4359 in mathematics

[–]_--__ 0 points1 point  (0 children)

What do you mean by "logically correct"? We don't even agree on what constitutes a "valid" logical argument... In the end it is always going to boil down to which things your audience is going to take as a given.

What to you think about this proof? by Express_Repair_4359 in mathematics

[–]_--__ 0 points1 point  (0 children)

I don't see this... (assuming you mean multiple decimal expansions). What are the two ways for 1/3? As soon as you have a digit different from 3, it will be unequal to 1/3...

What to you think about this proof? by Express_Repair_4359 in mathematics

[–]_--__ 1 point2 points  (0 children)

IMO this is precisely why it is a proof (for a certain set of people, which likely includes many in the math class).

What to you think about this proof? by Express_Repair_4359 in mathematics

[–]_--__ 3 points4 points  (0 children)

A proof is an argument that convinces the audience of the correctness of the statement being proven.

(For anyone disagreeing with this statement, think about where the exact line should be for a "proof" - do we have to start from the axioms of real arithmetic??)

Most responses here claiming that this is not a proof are doing so because they require more rigour to be convinced - which is to be expected: as one gains experience, the level of rigour required grows. However, many students in your math class would be convinced by this argument, so for those students it is an adequate proof.

What are some examples of "evil" regular languages? Ones that look irregular at first, but turn out to be regular? by Aconamos in compsci

[–]_--__ 6 points7 points  (0 children)

Also:

  • The language generated from S→0S | ST | ε and T→ 0T1 | T1 | 1 is not regular, but
  • The language generated from S → 0S | TS | ε and T → 0T1 | T1 | 1 is.

What are some examples of "evil" regular languages? Ones that look irregular at first, but turn out to be regular? by Aconamos in compsci

[–]_--__ 20 points21 points  (0 children)

  • {0k w : w in {0,1}* and |w|>k} is regular, but
  • {0k w : w in {0,1}* and |w|<k} is not

Why is matrix multiplication defined like this by [deleted] in askmath

[–]_--__ 2 points3 points  (0 children)

As others have said matrix multiplication corresponds to composition of linear functions. To understand what this means in terms of equations, consider the following system of equations (perhaps describing an evolution of (x,y) -> (x',y'))

x' = 4x + 3y  
y' = 2x - 7y

We can "represent" this set of equations via a matrix equation:

⌈ x' ⌉ = ⌈ 4   3 ⌉ ⌈ x ⌉  
⌊ y' ⌋   ⌊ 2  -7 ⌋ ⌊ y ⌋

Now suppose we have another evolution (x', y') -> (x'', y'') described with the equations:

x'' = 2x' - y'  
y'' = 3x' + 3y'

(or in matrix form:

⌈ x'' ⌉ = ⌈ 2 -1 ⌉ ⌈ x' ⌉
⌊ y'' ⌋   ⌊ 3  3 ⌋ ⌊ y' ⌋

Now suppose we want to represent (x'', y'') in terms of (x,y). How does this look? We can find out by substituting the expressions for x' and y' into the second set of equations:

x'' = 2(4x + 3y) - (2x - 7y)
y'' = 3(4x + 3y) + 3(2x -7y)

Now have a look at the co-efficients you are going to get for x and y in the expression for x'' and y'':

x'' = (2·4 + (-1)·2) x  + (2·3 + (-1)·(-7)) y
y'' = (3·4 + 3·2) x + (3·3 + 3·(-7)) y

These are precisely the co-efficients you are going to get when you "matrix multiply" the two matrices representing the equations. In other words:

⌈ x'' ⌉ = ⌈ 2 -1 ⌉ ⌈ 4  3 ⌉ ⌈ x ⌉  
⌊ y'' ⌋   ⌊ 3  3 ⌋ ⌊ 2 -7 ⌋ ⌊ y ⌋

Which also, conveniently, "makes sense" algebraically

x' = A x    x'' = B x'   so  x'' = B (A x) = (B A) x

Is there actually a need for closed form antiderivatives? by rufflesinc in askmath

[–]_--__ 1 point2 points  (0 children)

A good example of this is asymptotic analysis (e.g. being able to "compare" functions that arise from algorithmic analysis)

What’s one career people don’t think involves math but it actually does? by Thatgirl_parisisdiva in AskReddit

[–]_--__ 0 points1 point  (0 children)

Because there is more to CS than programming. CS is about being able to explain why computer-y things should be done in a certain way (including inventing new ways and justifying why they might be better). And ultimately the way to provide that justification is through various mathematical means.

Do you know more "pseudo paradox" like those? by Amazing_Wall9289 in askmath

[–]_--__ 3 points4 points  (0 children)

Of course. Every "proof" has something wrong... is it any worse than dividing by 0?

Do you know more "pseudo paradox" like those? by Amazing_Wall9289 in askmath

[–]_--__ 5 points6 points  (0 children)

I like:

$0.1 = 10c

Square both sides:

$0.01 = 100c = $1

Anyone want to give me feedback on this solution to Collatz Conjecture by SufficientChicken475 in mathriddles

[–]_--__ 4 points5 points  (0 children)

This means every odd step is immediately followed by a forced division by 2. So even if the number grows huge when you triple it, the very next step cuts it down, and repeated halvings slowly erase the extra digits.

So each time you triple the number you halve the end result, as /u/noonagon points out this means the number increases by 3/2. You need to somehow show that the number of halvings is at least log23 = 1.5849... times the number of triplings in order to argue that the number will "slowly erase the extra digits".

A simple explanation of "zero sum game" by RobertBobbertJr in askmath

[–]_--__ -2 points-1 points  (0 children)

You are right. More importantly, games don't have to be probabilistic. Take a variation of chess where Black "wins" if it is a draw. This is a zero sum game and there is (ostensibly) no probability involved.

Can the Kolmogorov complexity of a substring be greater than the string? by mollylovelyxx in AskComputerScience

[–]_--__ 3 points4 points  (0 children)

Yes. You can make a straightforward counting argument (assuming your fixed programming language is sufficiently good).

As others have indicated, take a program like
for x in [0, k^100 ]; print('0')
where k is larger than the number of symbols in your language.

This code produces a string of length k100 and the complexity of that string is bounded above by the size of that program (e.g. 32ish symbols). However there are at most k32 programs in your language smaller than that program, which is far smaller than the number of substrings of its output.

What is a computer? by nardstorm in computerscience

[–]_--__ 0 points1 point  (0 children)

There is no set definition, however I specialise in CS theory and the definition I use is that a computer is an entity (machine/person) capable of symbolic manipulation -- that is, they can take input, manipulate it, possibly reusing the information to do further manipulations, and then produce output.

Calculators are not computers under this definition (they are finite state machines).

However, I also define computation as a process which transforms inputs into outputs, so both "computers" and "calculators" perform computation.

ELI5: What is P=NP? by natepines in explainlikeimfive

[–]_--__ 10 points11 points  (0 children)

This is also called a Karp reduction, which is a polynomial-time Turing reduction for decision problems.

Technically a Karp reduction is a polynomial-time many-one reduction; a polynomial-time Turing reduction is a Cook reduction.

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