This proposition is true, but 40% of people get it wrong.
ysmemoirs “Every positive integer less than 1 is greater than 10000.”
This survey was so interesting that I did a little twisted survey myself.
nishio: for any positive integer x, “if x is less than 1, then x is greater than 1”…
- I was so taken aback by the number of “it doesn’t follow…” that I asked an additional question.
- One more question
explanation
- The top of all surveys is correct.
- logic
- 1: If P is false, then “if P then Q” is true regardless of the truth of Q
- 2: P = “x is less than 1” is false for any positive integer x
- 3: Thus “Q if P” is true for any positive integer x.
- If Q = “x is greater than 1”, it would be a questionnaire question text.
- Since the majority of the correct answers are “If 3 is even, then 4 is odd” at the end, many people understand 1: “If P is false, then Q is true regardless of the truth of Q”.
- It seems some people have judged “If x is less than 1, then x is greater than 1” to be “mathematically incorrect” or “a contradictory statement” based solely on this point.
- This is a mistake.
- For example, whether “1/(1/x)=x” is correct or not cannot be determined until x is specified as the source of any set.
- If it is a positive real number, it is correct because it does not contain zero, and if it is a whole real number, it is incorrect because it contains zero.
- Similarly, we can’t just look here to determine if “if x is less than 1, then x is greater than 1” is correct
- Those who made the decision prematurely must have implicitly assumed that x was a real number, etc., and made the decision.
Interesting Miscellaneous
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In France, zero is a number that is both positive and negative.”
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