How can you prove that 1 + 1 = 0?
you can prove that by using the[math]\displaystyle x=\sqrt{x^2}[/math][math]\displaystyle 1+1=2[/math][math]\displaystyle 1+1-1=2-1[/math][math]\displaystyle 1+1-1=\sqrt{(2-1)^2}[/math][math]\displaystyle 1+1-1=\sqrt{4-4+1}[/math][math]\displaystyle 1+1-1=\sqrt{0-0+1}[/math][math]\displaystyle 1+1-1=\sqrt{(0-1)^2}[/math][math]\displaystyle 1+1-1=0-1[/math][math]\displaystyle 1+1=0[/math]but it’s wrong because[math]\displaystyle x \neq \sqrt{x^2} [/math] but | [math]x | = \sqrt{x^2} [/math]
Why is 1-1+1-1+1-1+1...=1/2?
It depends.Let S= 1 - 1 + 1-....S = 0 + 1 - 1 + 1 - 1 ....S = (1 - 1) + 1 - 1 +...S = 1 - ( 1 -1 + 1 - 1 +...)S = 1 - S2S = 1 S = 1/2 . Note: This is just an average value. Actually, we can interpret the S as:S1 = (1-1) + ( 1-1) + ....Thus S1 = 0;Also , another interpretation could be: S2 = 1 -((1-1)+ (1-1) + (1-1)....)S2= 1So, S = average (S1, S2) = (1+0)/2 = 1/2
1+1+1+1+1+1+1+1+1+1+1+1 x 0+1=?
To evaluate the given numerical expression and thus answer this question, we need to consider the established order of operations in mathematics. Looking at this particular numerical expression, by the established order of operations, you first perform all multiplications and divisions in the order in which they appear from left to right and then perform all additions and subtractions in the order in which they appear from left to right; therefore, we have:1+1+1+1+1+1+1+1+1+1+1+1 x 0+1 = 1+1+1+1+1+1+1+1+1+1+1+ 0+1 = 11+0+1 = 11+1 = 12
How can I prove that 1 + 1 = 4?
This is simple enough to show, provided we break the rules of arithmetic altogether, and you obscure the violation well enough to slip past your target audience.An extremely simple method without any clever sleight of hand would be the following:Let a=02a=0 and 4a=02a=0=4aDividing both sides by a, we get:2=41+1=4This is called a mathematical fallacy, and 1+1=4 is an extraneous solution resulting from our violation of the associative rules of multiplication - namely the fact that we divided by zero when we divided both sides by the quantity ‘a’ (line 5).Reviewing the associative rule of multiplication can help us understand why division by zero is not generally allowed. Abusing this rule can lead to an infinite number of paradoxical conclusions, limited only by your imagination. For example, you could even prove that a unicorn is a cat. (Since you posted this in Calculus as well as Algebra, here is a similar extraneous solution using Calculus, which you can manipulate to whatever ends you wish: Mathematical fallacy - Wikipedia).Yet, there is still a sense in which the people answering your question with statements like “please get a life” are being more disrespectful to themselves than they are to you.While any proof that 1+1=4 would be a mathematical fallacy, there are some domains of knowledge for which it isn’t complete nonsense, and one of them was discussed at length by Buckminster Fuller.For example, if you are given three equally sized rods and asked to form a single equilateral triangle, the solution would be trivial. You could first lay out the rods end to end, so that together they lay in a straight line, then simply swing the terminating ends of the outer rods toward each other until they connect, forming 1 equilateral triangle.However, if you are given six equally sized rods (enough material for two equilateral triangles using the method above) and asked to form four equilateral triangles instead of two, things get interesting.First, think of a regular tetrahedron: it has four polyhedron vertices, six polyhedron edges, and four equivalent equilateral triangular faces.Note that it has four equilateral triangular faces (the result we want), using only six edges (the material we have).Buckminster Fuller’s drawing shows the rest:Depending on your goals and whatever constraints you were given at the beginning of the challenge, this could be a perfectly valid answer.1 triangle + 1 triangle = 4 triangles