in mathematical proofs, are you allowed to substitute numbers?
967058
It depends on what you are wanting to prove. Generally speaking, when you substitute numbers, you are restricting to a specific example. You cannot prove a general result by only looking at specific examples (unless you somehow show those specific cases give *all* the possibilities). However, you *can* show a result is false, if it is false for some specific example, so to show a general result is false, it is enough to 'plug in numbers'.
970218
Do you require mathematical signs, or are standard operations OK (like square root)?\n\n1: (1 + 1 + 1)!\n2: 2 + 2 + 2\n3: 3 * 3 - 3\n4: sqrt(4) + sqrt(4) + sqrt(4)\n5: 5 + 5/5\n6: 6 + 6 - 6\n7: 7 - 7/7\n8: 8 - sqrt(sqrt(8 + 8))\n9: 9/sqrt(9) + sqrt(9)\n\nAnd for a bonus: (0! + 0! + 0!)! = 6
845089
Ok, your question makes absolutely no sense.  Why say we can only use 1 through 16, and then say we can only use 1?\nSome ways, assuming I translated your question correctly, would include 16 + 16 +1 +1, and 16 + 15 + 3.... There are almost an infinite number of ways to add to 34 with the numbers 1-16, so please rephrase your question.
785570
try substituting letters for numbers and vice versa
7873
well in the demostrantion of the Real numbers...\n\nall the numbers and relations depend of the existence of 1... suck that there are some rules..\n\nso we even demostrate that 1 exists... and that 1 > 0... after that we can prove the existence of any other Real number..
961655
Yes, I can.  Quite simple actually.\n\nBut ask yourself if you know what these words mean:\n\n- integer\n- sum\n- difference\n- product  (think mathematics, not retail)\n- quotient
621145
With just ! (Factorial), +, -, * and /, it is impossible to get 150 using only 3 5s without the x^2 (Squared) operation (Which means x*x, in case you are in Fifth Grade), or using a '^2' as you say. If you say there is an alternate way, and there really is, then I give up and admit defeat. (I'm sure most others do.) If you are so sure, why don't you post the answer yourself?
467241
Add zero to anything and you get the same number you started with. It does not matter at which number you start with add 0 to it, it will still be zero. For example, you can start with 0 and add any number (n), lets say, you will still get that number n. Thus the notation for the previous example would be [0+n]. Ex. [0+1]=1 and again in the notation that you are asking about [0+n]=n, in the example above i just "substituted" 1, or just let [n] that represents any number for instances equal one. \n\nThe same goes for [n+0]=n, let [n] equal 1. add 1 to zero. What do you get? You should get one. see they (n+0 and 0+n )are the same thing.
120340
While it isn't possible, and all these "proofs" are fake (i.e. they contain a methematical error), I'll provide you one just for fun.\n\nLet a and b be two identical numbers (a = b)\n\na^2 = ab\na^2 + (a^2 - 2ab) = ab + (a^2 - 2ab)\n2(a^2 - ab) = a^2 - ab\n\nDividing both sides by (a^2 - ab) gives you\n\n2 = 1\n\n2 = 1 + 1 (common mathematical knowledge)\n\n2 = 2 + 1 (since 1 = 2)\n2 = 2 + 2 (again)\n1 + 1 = 2 + 2\n2 + 2 = 2 + 2\n1 + 1 + 2 = 2 + 2\n2 + 1 + 2 = 2 + 2\n5 = 2 + 2\n\n2 + 2 = 5
338816
As in many other pseudo-demonstrations of this kind, the error is to divide by zero (2-2) both sides of the identity. You can't do this because the division by zero is an undefined operation.\n\nFrom a well-known logic theorem, starting from a false statement, you can consistently derive any other false statement. This is the common source of many apparent paradoxes.
991053
Substitute or plug in the value for x an solve the problem using PEMDAS\n\nParentheses\nExponents\nMultiplication&\nDivision\nAddition&\nSubtraction
497917
No, the above answer is for BigInteger. BigDecimal allows you basically an infinite number of decimal places. Eliminates computational errors with floats and doubles in the IEEE standard
152234
1, 3, 5, 7, 11, 17....\n\n\nNumbers that can only be divided by that number or 1 with the result of a whole number.
16992
Adding 36 and 24 and subtracting 9 can easily be done in your head if you have graduated from elementary school.  Why someone couldn't is beyond me.
1143446
I do both of those and I also test numbers for divisibility.  My car license plate has as its numeric part the number 594 which is divisible by 11, that's how I remember my license plate number.  Also, when someone asks me to pick a number between 1 and 10, I usually pick pi, phi, or e, just to be a smart@$$.  They didn't say an INTEGER between 1 and 10, did they???
728920
mathematically speaking, incalculable arithmetic
57974
Not neccessarily. For instance, the square root of two (which is irrational) multiplied by the square root of two is two, which is very rational.\n\nGood Luck!\n\nP.S. Great Screenname. I love the phantom.