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What is proof by induction?
Mathematical induction is just a way of proving a statement to be true for all positive integers: prove the statement to be true about 1; then assume it to be true for a generic integer x, and prove it to be true for x + 1; it therefore must be true for all positive integers.
What is the smallest number that can be divisible by all integers?
There does not exist a number that is divisible by all integers. The opposite is true. The number one can divided into all integers.
Is it true no positive numbers are integers if so why?
It is not true.
Is it true that no positive number is an integer?
No, integers can be positive or negative.
Is it true that there are no integers that are whole numbers?
No, integers are positive and negative whole numbers
The product of two integers is positive. when is this statement true?
This statement is true when the two integers are positive, or when the two integers are negative.
Is this statement true if the product of two integers is divisible by 6 one of the integers is also divisible by 6?
That is false. This type of statement is only true for prime numbers, not for compound numbers such as 6. Counterexample: 2 x 3 = 6
What is proof by induction?
Mathematical induction is just a way of proving a statement to be true for all positive integers: prove the statement to be true about 1; then assume it to be true for a generic integer x, and prove it to be true for x + 1; it therefore must be true for all positive integers.
Prove that if x and y are positive integers then x square plus y square is even but not divisible by 4?
The statement cannot be proven because it is FALSE. If one of x and y is odd and the other is even then x2 + y2 MUST be odd. Also if x and y are even then x2 + y2 MUST be divisible by 4. The statement is only true if x and y are odd integers. Whether or not they are positive makes little difference.
What is the smallest number that can be divisible by all integers?
There does not exist a number that is divisible by all integers. The opposite is true. The number one can divided into all integers.
Are some rational numbers integers?
That's a true statement. Another true statement is: All integers are rational numbers.
What statement is TRUE about 16 and 212?
They are integers.
Is it true no positive numbers are integers if so why?
It is not true.
Is it true that no positive number is an integer?
No, integers can be positive or negative.
Is it true that there are no integers that are whole numbers?
No, integers are positive and negative whole numbers
If some Numbers are Integers and some Integers are Prime then all Numbers are definitely Prime This statement is true or false?
The statement is false.
Integers can be positive or negative true or false?
False - if the sentence is meant to be exhaustive. Integers can be positive or negative OR ZERO.
