hi therapist. you made a discussion with someone a long time ago, discussing that stuff like crunches and sit ups just make your gut bigger. what would be some abdominal exercises that don't do that?
actually, 90% of math graduates have an emotional breakdown from inability to find an answer and the other 10% (the ones that just picked a major at random) sit there eating cheetos and say "I dunno man, **** don't make sense."
Hmm? 1=3 mod 2. 0=2 mod 2. Let y be an integer and y+2=y mod 2. Let y be an integer and a be and integer and y+a=y (mod a).
You might be thinking of the computer science interpretation? I know I don't have the triple bar equals sign but (mod x) is usually taken to mean the whole equation. Even if you do consider the comp sci interpretation (that is, the boolean value of y+a==y%a), plugging in y=-a should yield true.
And as I went over in comments below no life without "mod 2" you can still consider things to be in the extended reals. en.wikipedia.org/wiki/Extended_real_number_line#Arithmetic_operations So there's plenty of mathematical things to say about a statement like this, "y+2=y" can have meaning depending on the context. (but in a field like the reals or complexes y+2=y is a contradiction)
Me and you man, me and you until the end. Second time I've tagged you and won't be the last. I'm a math major, so be assured that I will be using your username by accident for some time to come I shall defend mathematics until my dying breath against these casuals
Correct me if I'm wrong, but isn't the answer (positive or negative) infinity? (positive or negative) Infinity plus two is still (positive or negative) infinity.
The reason "infinity" usually isn't accepted as an answer is because the extended reals don't have a nice algebraic structure. From the same page: "With these definitions R is not a field, nor a ring, and not even a group or semigroup." These are useful structures in mathematics, but the lack of the structure doesn't make them useless. So, positive or negative infinity are solutions to x+2=x in the extended reals. What amegaara posted isn't a contradiction because infinity-infinity is meaningless as it is a statement disallowed in the extended reals (due to the lack of certain types of structure!).
But don't take my word for it, it's right there in the wiki page and is a matter of definition.
You said to correct you so here you go:
No, it is not infinity, what you are thinking of is if you ended up with 0 = 0 which would mean there are infinitely many solutions. But 0 = 8 means there are actually no solutions.
It is like saying potatoes = carrots. They do not, and never will, no matter how many there are
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because infinity is a concept, and not a number, infinity + 2 is still infinity. it's the exact same infinity (keep in mind, there are various levels of infinity, as you'll learn if you study the cardinality of the continuum).
the answer is not infinity, but not because of your second explanation
y+2=y
Since y contains the variable to solve for, move it to the left hand side of the equation by subtracting y from both sides
y+2-y=0
Since y and -y are like terms, add -y to get y to get 0
0+2=0
Remove the 0 from the polynomial, adding or subtracting 0 doesn't change the value of the expression
2=0
Since 2=/=0, there are no solutions
I think the content's solution is the same thing, but doesn't say it. You see that 8 =\= 0, so there's no possible number to make the equation true, so it is no solution.
Let a=b Multiply both sides by a giving:
a*a=a*b Now add a*a to both sides giving:
a*a + a*a = a*a + a*b Or, rewritten:
2a*a = a*a + a*b Now subtract 2a*b from both sides
2a*a - 2a*b = a*a + a*b - 2a*b Combine like terms on right
2a*a - 2a*b = a*a - a*b Factor out the a*a - a*b on each side
2(a*a - a*b) = 1(a*a - a*b) Cancel the (a*a - a*b) from both sides
2=1
But you wrote the multiplication wrong, and thats what I'm saying. Your math statement is incorrect, and that is my proof. Add more Parentheses to the written out exponents, and you'll see why its false
Y cannot equal 3
This is because you would come up with mixed numbers not full numbers. 5=3 would be 2.5 = 1.5 because you are splitting them in half.
Y+2=Y
3+2=3
5=3
2.5 = 1.5
This is also how it works with Y=2
Y+2=Y
2+2=2
4=2
2=1 you are taking half from 4 and that equals half of 2
I am just in 8th grade math, not algebra yet. so really, I don't think I could find any flaws yet. I thought you where useing a and b in places of y and 2 in the following equation given, therefor I was stateing with 8th grade mathmatics that it's really fairly simpiler then what you had. But I am now seeing that you are instad showing your own equation. I will figure out how that works soon. and I am too lazy to go back and fix all the spelling mistakes in this.
The flaw I used (and disguised) is dividing by zero. Which is a huge no-no. It takes place in the last step. When I say "cancel" what I'm really doing is dividing. The quantity I am "canceling" is a*a-a*b. So I am dividing by a*a-a*b which is actually equal to zero since a=b. We cannot divide by zero for complicated reasons, which are beyond 8th grade algebra cirriculum. Just notice that if dividing by 0 were admissible, then 2=1.
Infinity is a viable mathematical answer, it's just a never-ending, ever-growing number. (Or at least that is what my math teacher told me once, and it had to do with a certain high level type of math, which i forgot what it was called)
Infinity is NOT a number. It's not even an "ever-growing number", so.... there you go. And you might mean limits for infinity to be an answer, but not in this case.
the mathematical term in question here is not actually infinity but rather "infinite cardinal number" in this case y=infinite cardinal y meaning that y represents and infinite number since infinity itself is a concept not a number.
I get what you mean, rather than infinite, it's an infinite set of numbers/solutions or something similar. However, that's not what epiccore meant, hence why I refuted his statement. And even then, there is no solution to the equation anyways.
there are two solutions actually. 2=0 and y= inf.card.y which are mathematically correct. On a graph it would produce a vertical line ON the Y axis...in essence the answer IS the y axis.
That would be Gestalt_ Theory_, Gestalt Theorem states the whole is equal to or greater than the sum of its parts. this is best demonstrated through fraction/decimal conversion. For instance 1/3 = .3_ and 1/3 * 3 = 1 but .3_ * 3 = .9_ and .9_ < 1.
I assume the underscore "" means repeating? In that case, .999 (repeating) is NOT less than 1, but actually equals to 1. Remember .999 goes on forever, and we'll be going into the realm of limits and such.
essentially the implication is that they are considered equal because theres is no number between .9_ and 1, however .9_ is still less than one, some theorize that it is in how we measure them, much as when you try to measure a photon. Even if you know its there, it isnt if you measure it.
there is a solution. Y=Infinite Cardinal Y. a layman would simply say Y=Infinity, however since Infinity is a concept and not an actual number in and of itself then you have t identify that y is still a number so mathematically you would call it Infinite Cardinal Y which indicates that it is a number with an infinite value...more or less.
y + 2 = y
y - y = 2
(1-1) y = 2
y=2/(1-1) = 2/0 = lim x -> 1 (x+1)/(x-1) = lim x -> 0 (x+2)/x = 1+ 2/0 = 1 + 2/(2*0) = 1 + 1/0
let u = 1/0, y = 2u = 1+u => u = 1 => y = 2.
y - 2*y/2 = 1-½+⅓-¼+…+1/n (-1)^(n+1) + … = ln 2
y = (ln 2)/0
let s = 1/0 = 1/(1-1) = 1+1^1+1^2+1^3+1^4+…=1+1+1+1+1+…
let t = ½ = 1/(1-(-1))= 1-1+1-1+1-1+1-1+…
-t = -1+1-1+1-1+1-1+1-…
s - t = 1+1+1+1+1+1+1+1+…
-1+1-1+1-1+1-1+1-1+…
= 2+2+2+2+2+2+2+2+… [summing up each individual term]
= 2s
=> 1/0 = s = -t = -½
=> y = -(ln 2)/2. q.e.d.
What, are infinite series too complex for you? Fine. The Riemann zeta function has a pole at 1, but that's its only pole! 1+1+1+1+… = -½ and 1+2+3+4+… = -1/12, and those are rigorously calculated results. Check Wikipedia for a start.
It's only complex to a kid? Then why don't you have your million dollar prize for solving the Riemann hypothesis?
Those real valued solutions are only limits to an infinite sum. View it this way: the sum 1-½+⅓-¼+1/5-1/6+… can either be summed to ln 2 or be manipulated to limit to ½ ln 2 in infinite terms (check the Wikipedia page of the sum for that). Call the sum s and you'll see that 4s/(ln 2) can either be 4 or 2. Therefore 4s/(ln 2) solves the equation y + 2 = y.
Okay so peeps are saying we can't substitute in infinity, but if we take the limit as y goes to +/- infinity then the equation would make sense and y=y. Super simple stuff.
also buying wet dream potions