when x >= 0 , y >= 0, and y must exceed x by at most 200, does it imply y > x?

Question

The statement below: y must exceed x by at most 200 can be written as y - x <= 200 Does the statement imply y must exceed x? y > x ?

For my understanding: y must exceed x by at most 200

this statement is formed by 2 statements below:

1. y must exceed x or y must be more than x
2. y - x <= 200

ChatGPT state that it only show the difference must not be more than 200.

My main problem is that some said the statement imply y > x, some said not. So, what is the answer?

Answer 1

TL;DR

Yes, as written y must be greater than x. You could write separate checks for each condition, but your simplification seems valid.

However, how you compare your values properly will depend on whether you have to account for non-Integers or negative numbers. If you're only dealing with positive whole numbers then you just need to ensure y is 1..200 more than x in any way that suits you.

Various Solutions Based on Differing Assumptions

You didn't tag your original question with a language tag, so there's likely more than one way to express this. I'll provide some Ruby solutions.

Comparable Numeric Objects

The following will work with most Numeric objects but requires a separate check to ensure the difference isn't exactly zero.

abs_diff = (y - x).abs
p abs_diff.nonzero? && abs_diff <= 200

This basic solution worked for me in casual testing, but it's meant to be simple rather than fail-safe.

Best Option for Arbitrary Precision Values

Since a Float isn't reliable for non-Integers, or if you need to account for arbitrary precision values, you can compare BigDecimal or Real numbers instead. Additionally, you must also specifically check that the absolute difference isn't exactly zero rather than using a Range with an imprecise floor. For example, this should work reliably with non-imaginary Numeric values:

require "bigdecimal"
require "bigdecimal/util"

min = BigDecimal("0.0")
max = BigDecimal("200.0")

# Use BigDecimal to ensure arbitrary precision,
# to validate the absolute difference.
abs_diff = (y.to_d - x).abs
p abs_diff > min && abs_diff <= max

Checking that the difference is both non-zero and less-than-or-equal-to 200 just seems easier, safer, and more flexible to me. That's why the BigDecimal option above would be my preferred solution, but it may be overkill for your specific data. Your mileage may therefore vary.