# Peano's Postulates Proofs

How can I prove the following two questions:

Prove using Peano's Postulates for the Natural Numbers that if a and b are two natural numbers such that a + b = a, then b must be 0?

Prove using Peano's Postulates for the Natural Numbers that if a and b are natural numbers then: a + b = 0 if and only if a = 0 and b = 0?

I understand the basic postulates, but not sure how to apply them to these specific questions. The questions seem so basic and obvious, but when it comes to applying the postulates I am lost.

-

1
Is this homework? If so, please add the homework tag. – Ben Crowell Oct 14 '12 at 22:22
@BenCrowell homework tag added, sorry. – Jakemmarsh Oct 16 '12 at 21:24

## 1 Answer

Use induction on $a$ for the first. Use case analysis (4 cases: $a = Z$ or $Sx$, $b = Z$ or $Sy$) for the second.

-

I think I figured out the first one, but this answer hasn't really clarified anything for me. – Jakemmarsh Oct 16 '12 at 21:19
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.899405300617218, "perplexity_flag": "head"}