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  1. Jul 16, 2014 · No, strictly, they do not convey the same meaning. In practice, your second sentence is often used to mean the first. I believe x does not equal y means that you actually hold a belief about the inequality of x and y. I don't believe that x equals y simply means that a belief about the equality exists, but you do not share that belief.

  2. 1 = x/x for all x not equal to 0, and defining 0/0 = 1 makes that true for all x. Both of these arguments are equally valid (and there are similar equally valid arguments for literally every other possible value, including +infinity and -infinity).

  3. Sep 1, 2013 · To prove it rigorously, show that a contradiction arises when you assume x0 x0 and y0 y0 and xy = 0 x y = 0. One way to do this is to assume that xy = 0 x y = 0 and x0 x0, and then show that y = 0 y = 0. Hint: Suppose that x0 x0 and xy = 0. x y = 0.

  4. Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

  5. Apr 21, 2013 · x % 2 gives the remainder after the integer division (when dealing with only integers such as in this case, otherwise a common type) of x/2. The % is called the modulo operator. Of course when the remainder is 0, the number is even.

  6. We can often solve inequalities by adding (or subtracting) a number from both sides (just as in Introduction to Algebra), like this: If we subtract 3 from both sides, we get: And that is our solution: x < 4. In other words, x can be any value less than 4. What did we do?

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  8. If x=y, x and y represent the same value or thing. If xy, x and y are almost equal. If xy, x and y do not represent the same value or thing. If x<y, x is less than y. If x>y, x is greater than y. If xy, x is much less than y. If xy, x is much greater than y. If xy, x is less than or equal to y. If xy, x is greater than or equal to y.

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