prove that there is a real number between any two real numbers, explain nicely plz,?

Answer 1

Two real numbers have the distance between them sliced asunder. What lieth in the slice? Yea, it could be nothing else but the sum of those two real numbers (itself a real number, to be sure), divided by 2. And no real number loses it's reality by being divided by 2.

I think that was rather nicely put, if I do say so myself. ;)

Answer 2

I'm not sure if you're looking for a formal proof, but an easy way to think about it is that you can take two numbers, like 0 and 1, and just take the midpoint between them, so 1/2. You can continue this process indefinitely using 0 and your previous midpoint, and find the new midpoint. Of course, there are infinitely many other numbers between 0 and 1, but the midpoint just serves to simplify the problem.

Answer 3

hmmm...

let x be a real number
let y be a real number.

let's find the midpoint between these numbers

mdpoint = y + x / 2

because addition is closed (an advanced concept which means simply that adding two real numbers gives you a real number)

dividing this real number by 2 will give you a real number between x and y since the the midpoint formula is really the same formula for calculating the average of 2 numbers.

hope this helps...



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Answer 4

do you mean like between 1 and 2 is 1.5 and between 4 and 5 is 4.5 because the numbers between are real numbers but just in fraction or decimals because it's not a whole number unfortunately.

Answer 5

real numbers can be infinite, so no matter what two you pick, say 8.673884 and 8.673885, you can always just add another number to make it in between, 8.6738847 for example, you never run out of room. Hopefully that's what you're looking for.

Answer 6

let x and y be 2 real numbers.

(x+y)/2 is one real number between x & y.