write an equation that describes the positive real number closest to zero?

Question

Write an equation where x is positive, real, and approaches zero.

Answer 1

y = lim x
..... x→0+

This should read: y equals the limit of x as x approaches 0 from above. I put in some periods on the second line to try and make the term x->0+ line up under the limit operator properly.

This is a "concept" equation in that you can always find a closer positive real number to zero, but that is how the limit concept works.

Answer 2

R = Reals

Postive R: 0 < x _< 1

Can't write the at or less sign very well on here. It is basically < with a line below it.

So,the equation I wrote above is stating that x is greater than zero but at or less than one.

Be sure to put the "R" in there because this states x is positive real numbers.

Answer 3

There is no closest real number to zero, just like there's no maximum real number. This is the realm of infinitesimals.

This can be demonstrated as follows. Presume that x is the smallest positive real number. However, x/2 would be smaller, which leads to the RAA contradiction.

Answer 4

x= 1-0.999 (dot above nine would make it repetitive to an infinite number of places) It is a good question from the point of view of language as most other answers have been inequalities and therefore not équations'.

Answer 5

0 x*10^n n is any -ve no. and |n| should be big till infinity

Answer 6

kinda hard with typing since you've got limited symbols