In mathematical writing, we should not start a sentence with a symbol or a formula. Choose the sentences that don't make this mistake.

Question

BlackTom AI · Accepted Answer

Mathematical prose should present a grammatically complete sentence beginning with words (a subject or introductory phrase), not with a lone symbol or formula. This maintains readability and standard sentence structure.

Relevant knowledge points and concepts:
- A sentence should begin with a word (noun, article, pronoun, etc.) rather than a mathematical symbol or formula.
- Beginning with a symbol (like f or an equation) is stylistically discouraged because it breaks grammatical flow.
- In multiple-answer questions, evaluate each choice independently against this rule.

Step-by-step reasoning for each choice:
a. "f is continuous on [0,1]." — This starts with the symbol f. Although mathematically understandable, it violates the style rule because the sentence begins with a symbol rather than a word. Therefore (a) is incorrect.

b. "The function f is continuous on [0,1]." — This begins with the word phrase "The function," which provides a grammatical subject. The symbol f appears later in the sentence. This follows the style rule, so (b) is correct.

c. "∴ the function f is continuous on [0,1]." — The sentence begins with the symbol "∴" (therefore). Starting a sentence with such a symbol is stylistically wrong; proofs may use it inline, but not as the first character of a sentence. Thus (c) is incorrect.

d. "x^2 − 3x + 2 = 0 has two solutions x = 1 and x = 2." — This begins with the formula "x^2 − 3x + 2 = 0." Starting a sentence with a formula breaks the rule; a word-based introduction like "The equation ..." is preferred. Hence (d) is incorrect.

e. "The equation x^2 − 3x + 2 = 0 has two solutions x = 1 and x = 2." — This begins with the word "The" and the noun "equation," giving a grammatical subject; the formula appears later. This conforms to the guideline, so (e) is correct.

Why the correct answers are correct:
- Both (b) and (e) start with words that serve as grammatical subjects ("The function" and "The equation"), so they do not begin with symbols or formulas and therefore follow mathematical writing conventions.

Why the others are incorrect:
- (a) and (d) start directly with symbols/formulas; (c) starts with a proof symbol. All violate the “do not start a sentence with a symbol or formula” rule.

Conclusion: The correct choices are (b) and (e), matching the provided answer.

In mathematical writing, we should not start a sentence with a symbol or a formula. Choose the sentences that don't make this mistake.多项选择题

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