The question asks to identify the false statement among the given options concerning basic number sets.
Analyzing Number Set Statements
Statement 1: All natural numbers together with zero are called integers.
- Natural Numbers are typically defined as {1, 2, 3, ...}.
- Whole Numbers are defined as {0, 1, 2, 3, ...}.
- Integers are defined as {..., -2, -1, 0, 1, 2, ...}.
- Natural numbers combined with zero ({0, 1, 2, 3, ...}) form the set of whole numbers, not integers.
- Therefore, this statement is False.
Statement 2: There is no largest natural number.
- The set of natural numbers {1, 2, 3, ...} extends infinitely.
- For any natural number n, n + 1 is also a natural number.
- Thus, there is no maximum value.
- This statement is True.
Statement 3: There is no largest whole number.
- The set of whole numbers {0, 1, 2, 3, ...} also extends infinitely.
- For any whole number w, w + 1 is also a whole number.
- Therefore, there is no largest whole number.
- This statement is True.
Statement 4: 1 is the smallest natural number.
- Based on the common definition where natural numbers start from 1 ({1, 2, 3, ...}), the smallest number is indeed 1.
- This statement is True.
Conclusion
The only statement found to be false is the first one, which incorrectly defines the set of natural numbers plus zero.
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Important Questions from Number System
What is the value of 1 2 + 2 2 + 3 2 + ......21 2 ?
Which sequence is correct to represent the hierarchical chain of number system?
(Where N - Natural Numbers
W - Whole Numbers
Q - Rational Numbers
Z - Integers)
What must be added to 45680 to make it exactly divisible by 9?
How many zeroes are there at the end of the following product?
1 x 5 x 10 x 15 x 20 x 25 x 30 x 35 x 40 x 45 x 50 x 55 x 60
Let XYZ be a three-digit number, where (x + y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by
