Final answer:
To rewrite the given statement, the missing phrase is 'less than or equal to every positive integer.' This is because the smallest positive integer is 1.
Step-by-step explanation:
The statement to be rewritten is: 'There is a positive integer that is less than or equal to every positive integer.' The correct way to fill in the blanks for the statement 'There is a positive integer m such that m is ____.' would be 'less than or equal to every positive integer.' This is because the smallest positive integer is 1, and there cannot be a positive integer less than 1. Therefore, 1 is the number that is less than or equal to every positive integer.