The number of all natural numbers up to 1000 with non-repeating digits is:

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To calculate the number of natural numbers up to 1000 with non-repeating digits, we consider numbers with 1, 2, and 3 digits separately.

#### Step 1: Single-digit numbers
All single-digit numbers (1 to 9) have non-repeating digits. Hence, there are:  
$$ 9 $$ such numbers.

#### Step 2: Two-digit numbers
For two-digit numbers:  
- The first digit (tens place) can be any digit from 1 to 9 (non-zero).  
- The second digit (units place) can be any digit except the first digit.

Thus, the total number of two-digit numbers is:  
$$ 9 	imes 9 = 81. $$

#### Step 3: Three-digit numbers
For three-digit numbers:  
- The first digit (hundreds place) can be any digit from 1 to 9 (non-zero).  
- The second digit (tens place) can be any digit except the first digit.  
- The third digit (units place) can be any digit except the first two digits.

Thus, the total number of three-digit numbers is:  
$$ 9 	imes 9 	imes 8 = 648. $$

#### Step 4: Total count
Adding all these cases together:  
$$ 	ext{Total} = 9 + 81 + 648 = 738. $$

Thus, the total number of natural numbers up to 1000 with non-repeating digits is **738**.

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