Definition
Assumption
An assumption is a condition treated as true while a mathematical model or argument is used.
Continue from this idea into connected AXIO math.
Defining relationship
Write the starting rule before trusting the finish.
An assumption is a condition treated as true for the purpose of a mathematical model or argument. A conclusion is supported only within the assumptions used to reach it, and those assumptions may need checking or revision.
- 1
ASSUMPTION
The rate stays constant
Treat 3 litres per minute as true for all six minutes.
- 2
REASONING
Use the stated condition
Six equal one-minute intervals use the same rate.
- 3
CONCLUSION
18 litres—within that assumption
If the flow slows, the conclusion no longer describes what happened.
State the condition before using the result.
What it means
An assumption is a starting rule for this problem, not a fact that must be true forever. It lets the reasoning move forward. Good mathematical work says what the starting rule is and checks whether it fits the real situation.
Remember it
Write the starting rule before trusting the finish.
Example
A tank receives water at 3 litres per minute. Assuming the rate stays constant, it receives 3 × 6 = 18 litres in six minutes. If the flow slows down, the calculation no longer describes what really happened.
Watch for
An assumption may be useful without being certain, but a hidden or false assumption can make a conclusion unreliable.
Common mix-up
A guess proposes an answer. An assumption supplies a condition that the reasoning starts from.
Exact meaning
An assumption is a condition treated as true for the purpose of a mathematical model or argument. A conclusion is supported only within the assumptions used to reach it, and those assumptions may need checking or revision.